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Mth603- First Quizzes (11-11-2011)

Question : While solving a system of linear equations, which of the following approach is economical for the computer memory?

Select correct option:

Direct

Iterative

Analytical

Graphical

Question :The basic idea of relaxation method is to reduce the largest residual to ………….

Select correct option:

One

Two

Zero

None of the given choices

Question:   The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.

Select correct option:

main diagonal

last column

last row

first row

Question: If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix ,

the eigenvalues of A are the diagonal entries of A.

Select correct option:

TRUE

FALSE

Question :  A 3 x 3 identity matrix have three and different eigen values.

Select correct option:

TRUE

FALSE

Question :  Which of the following is a reason due to which the LU decomposition of the system of linear equations; x+y = 1, x+y =2 is not possible?

Select correct option:

Associated coefficient matrix is singular

All values of l’s and u’s can’t be evaluated

Determinant of coefficient matrix is zero

All are equivalent

Question :  Gauss - Jordan Method is similar to ……….

Select correct option:

Gauss–Seidel method

Iteration’s method

Relaxation Method

Gaussian elimination method

Question  : While using Relaxation method, which of the following is the largest Residual for 1st iteration on the system; 2x+3y = 1, 3x +2y = - 4 ?

Select correct option:

-4

3

2

1

Question : Gauss–Seidel method is also known as method of …………….

Select correct option:

Successive displacement

Iterations

False position

None of the given choices

Question  : Jacobi’s Method is a/an………………

Select correct option:

Iterative method

Direct method

Question : The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the given 3 x 3 identity matrix. where symbol ^ shows power.

Select correct option:

(x-1)^3

(x+1)^3

x^3-1

x^3+1

Question : The Power method can be used only to find the eigenvalue of A that is largest in absolute value—we call this eigenvalue the dominant eigenvalue of A.

Select correct option:

TRUE

FALSE

Question: In …………… method, a system is reduced to an equivalent diagonal form using elementary transformations.

Select correct option:

Jacobi’s

Gauss-Seidel

Relaxation

Gaussian elimination

Question : The linear equation: 2x+0y-2=0 has -------- solution/solutions.

Select correct option:

unique

no solution

infinite many

finite many

Question : Under elimination methods, we consider, Gaussian elimination and ……………methods.

Select correct option:

Gauss-Seidel

Jacobi

Gauss-Jordan elimination

None of the given choices

Question : Which of the following method is not an iterative method?

Select correct option:

Jacobi’s method

Gauss-Seidel method

Relaxation methods

Gauss-Jordan elimination method

Question : An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal

to zero.

Select correct option:

TRUE

FALSE

Question : Exact solution of 2/3 is not exists.

Select correct option:

TRUE

Page No.72

FALSE

Question : When the condition of diagonal dominance becomes true in Jacobi’s Method.Then its means that the method is …………….

Select correct option:

Stable

Unstable

Convergent

Divergent

Question :  Gauss–Seidel method is similar to ……….

Select correct option:

Iteration’s method

Regula-Falsi method

Jacobi’s method

None of the given choices

Question :  Sparse matrices arise in computing the numerical solution of …………….

Select correct option:

Ordinary differential equations

Partial differential equations

Linear differential equations

Non-linear differential equations

Question : While solving by Gauss-Seidel method, which of the following is the first Iterative solution for the system; x-2y =1, x+4y=4 ?

Select correct option:

(1, 0.75)

(0,0)

(1,0)

(0,1)

Question:  While solving a system of linear equations by Gauss Jordon Method, after all the elementary row operations if there lefts also zeros on the main diagonal then which of the is true about the system?

Select correct option:

System may have unique solutions

System has no solution

System may have multiple numbers of finite solutions

System may have infinite many solutions

Question:    Numerical methods for finding the solution of the system of equations are classified as direct and ………… methods

Select correct option:

Indirect

Iterative

Jacobi

None of the given choices

Question : If the Relaxation method is applied on the system; 2x+3y = 1, 3x +2y = - 4, then largest residual in 1st iteration will reduce to -------.

Select correct option:

zero

4

-1

-1

Question :   While using Relaxation method, which of the following is the Residuals for 1st iteration on the system; 2x+3y = 1, 3x +2y =4 ?

Select correct option:

(2,3)

(3,-2)

(-2,3)

(1,4)

Question : If the order of coefficient matrix corresponding to system of linear equations is 3*3 then which of the following will be the orders of its decomposed matrices; ‘L’ and ‘U’?

Select correct option:

Order of ‘L’ = 3*1, Order of ‘U’ = 1*3

Order of ‘L’ = 3*2, Order of ‘U’ = 2*3

Order of ‘L’ = 3*3, Order of ‘U’ = 3*3

Order of ‘L’ = 3*4, Order of ‘U’ = 4*3

Question : While solving the system; x–2y = 1, x+4y = 4 by Gauss-Seidel method, which of the following ordering is feasible to have good approximate solution?

Select correct option:

x+4y = 1, x-2y = 4

x+2y = 1, x- 4y =4

x+4y = 4, x–2y = 1

no need to reordering

Question : Full pivoting, in fact, is more ……………than the partial pivoting.

Select correct option:

Easiest

Complicated

Question : Gauss–Seidel method is also known as method of …………….

Select correct option:

Successive displacement

Iterations

False position

None of the given choices

Question : For the equation, the root of the equation lies in the interval......

► (1, 3)

► (1, 2)

► (0, 1)

► (1, 2)

Question :-............lies in the category of iterative method.

► Bisection Method

► Regula Falsi Method

► Secant Method

► all of the given choices

Question : Power method is applicable if the eigen vectors corresponding to eigen values are

linearly independent.

True

1. false

Question:  A 3 x 3 identity matrix have three and different eigen values.

1. True

False

Question : If n x n matrices A and B are similar, then they have the different eigenvalues (with the same multiplicities).

1. True

False

Question : The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____zeros along its main diagonal.

No

1. At least one

Question : An eigenvector V is said to be normalized if the coordinate of largest magnitude is

equal to ______.

Unity

1. zero

Question : If the root of the given equation lies  between a and b, then the first approximation to the root  of the equation by bisection method is ……

►

►

►

► None of the given choices

Question : To apply Simpson’s 3/8 rule, the number of intervals in the following must be

► 10

► 11

► 12

► 13

Question : The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric________ definite matrices A.

Select correct option:

positive

negative

Question : Differences methods find the ________ solution of the system.

Select correct option:

numerical

Analytical

Question : To apply Simpson’s 1/3 rule, the number of intervals in the following must be

► 2   (Simpson''s 1/3 rule must use an even number of elements')

► 3

► 5

► 7

Question : The Power method can be used only to find the eigenvalue of A that is largest in absolute value we call this eigenvalue the dominant eigenvalue of A.

Select correct option:

TRUE

FALSE

Question : The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.

Select correct option:

main diagonal

last column

last row

first row

Question : Bisection and false position methods are also known as bracketing method and are

always

Divergent

Convergent

Page No.67

Question  : The Inverse of a matrix can only be found if the matrix is

Singular

Every square non-singular matrix will have an inverse.

Scalar

Diagonal

Question : In interpolation is used to represent the δ

Forward difference Δ

Central difference

Backward difference

Question : The base of the decimal system is _______

10

0

2

8

None of the above.

Question  : Bisection method is ……………….. method

► Open Method

► Bracketing Method

Question : Exact solution of 2/3 is not exists.

TRUE

FALSE

Question : The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____zeros along its main diagonal.

No

atleast one

Question: A 3 x 3 identity matrix have three and __________eigen values.

same

different

Question : Eigenvalues of a symmetric matrix are all _______ .

real

complex

zero

positive

Question : The Jacobi iteration converges, if A is strictly diagonally dominant.

TRUE

FALSE

Question : Below are all the finite difference methods EXCEPT _________.

jacobi’s method

newton's backward difference method

Stirlling formula

Forward difference method

Question:  If n x n matrices A and B are similar, then they have the same eigenvalues (with the same multiplicities).

TRUE

FALSE

Question : If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A.

TRUE

FALSE

Question: The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the given 3 x 3 identity matrix. where symbol ^ shows power.

(x-1)^3

(x+1)^3

x^3-1

x^3+1

Question : Two matrices with the same characteristic polynomial need not be similar.

TRUE

FALSE

Page No.69

Question : The determinant of a diagonal matrix is the product of the diagonal elements.

True

1. False

Qusetion : The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric

positive definite matrices A.

True

1. False

Question : The determinant of a _______ matrix is the product of the diagonal elements.

Page No.70

Diagonal

1. Upper triangular

2. Lower triangular

3. Scalar

Question : For differences methods we require the set of values.

True

False

Question : If x is an eigen value corresponding to eigen value of V of a matrix A. If a is any constant, then x – a is an eigen value corresponding to eigen vector V is an of the matrix A - a I.

True

False

Question : Central difference method seems to be giving a better approximation, however it requires more computations.

Page No.71

True

False

Question : Iterative algorithms can be more rapid than direct methods.

True

1. False

Question : Central Difference method is the finite difference method.

True

1. False

Question : Back substitution procedure is used in …………….

Select correct option:

Gaussian Elimination Method

Jacobi’s method

Gauss-Seidel method

None of the given choices

Question : The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal.

True

False1.

Question: The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.

main diagonal

last column

last row

first row

Question : .An eigenvector V is said to be normalized if the coordinate of largest magnitude is equalto ______.

Unity

Zero

Question : An eigenvector V is said to be normalized if the coordinate of largest magnitude is equalto zero.

TRUE

FALSE

Question : .The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.

True

False

Question : The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetricdefinite matrices A.

Pos I t ive

Negative

Question : .The determinant of a diagonal matrix is the product of the diagonal elements.

True

False1

Question : Power method is applicable if the eigen vectors corresponding to eigen values are linearlyindependent.  www.vustudents.ning.com

True

False

Question : Power method is applicable if the eigen values are ______________.

real and distinct

real and equal

positive and distinct

negative and distinct

Question : Simpson’s rule is a numerical method that approximates the value of a definite integral by using polynomials.

Linear

Cubic

Quartic

Question : .In Simpson’s Rule, we use parabolas to approximating each part of the curve. This provesto be very efficient as compared to Trapezoidal rule.

True

False

Question : The predictor-corrector method an implicit method. (multi-step methods)

True

False

Question : Generally, Adams methods are superior if output at many points is needed.

True

False

Question : The Trapezoidal rule is a numerical method that approximates the value of a.______________.

Indefinite integral

Definite integral

Improper integral

Function

Question : The need of numerical integration arises for evaluating the definite integral of a functionthat has no explicit ____________ or whose antiderivative is not easy to obtain.

Anti deri vat ive

Derivatives.

Question : .An indefinite integral may _________ in the sense that the limit defining it may not exist.

diverge

Converge

Question : An improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or  ∞ or -∞ or, in some cases, as both endpoints approach limits.

TRUE

FALSE

Question : Euler's Method numerically computes the approximate derivative of a function.

TRUE

FALSE

Question :.Euler's Method numerically computes the approximate ________ of a function.

Antiderivative

Derivative

Error

Value

Question: If we wanted to find the value of a definite integral with an infinite limit, we can insteadreplace the infinite limit with a variable, and then take the limit as this variable goes to _________.

Chose the correct option :

Constant

Finite

Infinity

Zero

Question : Euler's Method numerically computes the approximate derivative of a function.

TRUE

FALSE

Question: .The Jacobi iteration ______, if A is strictly diagonally dominant.

converges

Diverges

Question :.Two matrices with the same characteristic polynomial need not be similar.

TRUE

fALSE

Question :.Differences methods find the ________ solution of the system.

Nu me rical

Analytica

Question : .By using determinants, we can easily check that the solution of the given system of linear equation exits and it is unique.

TRUE

FALSE

Question : The absolute value of a determinant (|detA|) is the product of the absolute values of theeigenvalues of matrix A

TRUE

FALSE

Question : Eigenvectors of a symmetric matrix are orthogonal, but only for distinct eigenvalues.

TRUE

FALSE

.

Question : Let A be an n ×n matrix. The number x is an eigenvalue of A if there exists a non-zerovector v such that _______.

Av = xv

Ax = xv     not shore

Av + xv=0

Av = Ax1

Question : In Jacobi’s Method, the rate of convergence is quite ______ compared with other methods.

slow

Fast

Question : .Numerical solution of 2/3 up to four decimal places is ________.

0.667

0.6666

0.6667

0.666671.

Question : Symbol used for forward differences is

∆   Correct

δ

µ

Question : .The relationship between central difference operator and the shift operator is given by

δ =Ε−Ε-1

δ = Ε+Ε-1

δ = Ε1/2+Ε1/2

δ = E1/2 −Ε1/2

Question : Muller’s method requires --------starting points

1

2

3

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Question : By using determinants, we can easily check that the solution of the given system of linear equation ______ and it is ______.

Select correct option:

exits, unique

exists, consistent

trivial, unique

nontrivial, inconsistent

Question : Two matrices with the _______ characteristic polynomial need not be similar.

Select correct option:

same

different

Question :  In ……………… method, the elements above and below the diagonal are simultaneously made zero.

Select correct option:

Jacobi’s

Gauss-Seidel

Gauss–Jordon Elimination

Relaxation

Question : Which of the following is equivalent form of the system of equations in matrix form; AX=B ?

Select correct option:

XA = B

X = B(Inverse of A)

X =(Inverse of A)B

BX = A

Question : If the determinant of a matrix A is not equal to zero then the system of equations will have……….

Select correct option:

a unique solution

many solutions

infinite many solutions

None of the given choices

Question :  Sparse matrix is a matrix with ……….

Select correct option:

Some elements are zero

Many elements are zero

Some elements are one

Many elements are one

Question : An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to zero.

Select correct option:

TRUE

FALSE

MTH603 – 2ND QUIZ FILE (24-11-2011)

QUIZ.NO.1

Question # 1 of 10 ( Start time: 11:14:39 PM ) Total Marks: 1

The Jacobi iteration ______, if A is strictly diagonally dominant.

Select correct option:

=>converges

diverges

Question # 2 of 10 ( Start time: 11:16:04 PM ) Total Marks: 1

The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____ zeros along its main diagonal.

Select correct option:

=>no

atleast one

Question # 3 of 10 ( Start time: 11:17:14 PM ) Total Marks: 1

Power method is applicable if the eigen vectors corresponding to eigen values are linearly _______.

Select correct option:

=>independent

dependent

Question # 4 of 10 ( Start time: 11:17:42 PM ) Total Marks: 1

Power method is applicable if the eigen values are ______________.

Select correct option:

real and distinct

real and equal

positive and distinct

negative and distinct

Question # 5 of 10 ( Start time: 11:18:07 PM ) Total Marks: 1

How many Eigen vectors will exist corresponding to the function; Exp(ax) = e^ax, when the matrix operator is of differentiation?

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Select correct option:

Infinite many

Unique

Finite Multiple

None

Question # 6 of 10 ( Start time: 11:18:26 PM ) Total Marks: 1

By using determinants, we can easily check that the solution of the given system of linear equation ______ and it is ______.

Select correct option:

exits, unique

exists, consistent

trivial, unique

nontrivial, inconsistent

Question # 7 of 10 ( Start time: 11:19:55 PM ) Total Marks: 1

The determinant of a diagonal matrix is the product of the diagonal elements.

Select correct option:

=>TRUE

FALSE

Question # 8 of 10 ( Start time: 11:21:14 PM ) Total Marks: 1

For differences methods we require the set of values.

Select correct option:

=>TRUE

FALSE

Question # 9 of 10 ( Start time: 11:22:29 PM ) Total Marks: 1

Eigenvectors of a symmetric matrix are orthogonal, but only for distinct eigenvalues.

Select correct option:

TRUE

FALSE

Question # 10 of 10 ( Start time: 11:23:55 PM ) Total Marks: 1

Two matrices with the _______ characteristic polynomial need not be similar.

Select correct option:

=>same

different

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

QUIZ.NO.2

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Question # 1 of 10  Total Marks: 1

While using Relaxation method, which of the following is the Residuals for 1st iteration on the system; 2x+3y = 1, 3x +2y =4 ?

Select correct option:

(2,3)

(3,-2)

(-2,3)

(1,4)

Question # 2 of 10 ( Start time: 11:14:32 PM ) Total Marks: 1

Sparse matrices arise in computing the numerical solution of …………….

Select correct option:

Ordinary differential equations

Partial differential equations

Linear differential equations

Non-linear differential equations

Question # 3 of 10 ( Start time: 11:15:18 PM ) Total Marks: 1

In ……………… method, the elements above and below the diagonal are simultaneously made zero.

Select correct option:

Jacobi’s

Gauss-Seidel

=>Gauss–Jordon Elimination

Relaxation

Question # 4 of 10 ( Start time: 11:16:25 PM ) Total Marks: 1

If the order of coefficient matrix corresponding to system of linear equations is 3*3 then which of the following will be the orders of its decomposed matrices; ‘L’ and ‘U’?

Select correct option:

Order of ‘L’ = 3*1, Order of ‘U’ = 1*3

Order of ‘L’ = 3*2, Order of ‘U’ = 2*3

Order of ‘L’ = 3*3, Order of ‘U’ = 3*3

Order of ‘L’ = 3*4, Order of ‘U’ = 4*3

Question # 5 of 10 ( Start time: 11:17:54 PM ) Total Marks: 1

Which of the following is equivalent form of the system of equations in matrix form; AX=B ?

Select correct option:

XA = B

=>  X = B(Inverse of A)

X =(Inverse of A)B

BX = A

Question # 6 of 10 ( Start time: 11:19:00 PM ) Total Marks: 1

Which of the following rearrangement make strictly diagonal dominant, the system of linear equations; x-3y+z= –2, –6x+4y+11z=1, 5x–2y–2z=9?

Select correct option:

5x–2y–2z=9, x–3y+z= –2, –6x+4y+11z=1

–6x+4y+11z=1, x–3y+z= –2, 5x–2y–2z=9

5x–2y–2z=9, –6x+4y+11z=1, x–3y+z= –2

No need to rearrange as system is already in diagonal dominant form.

Question # 7 of 10 ( Start time: 11:20:24 PM ) Total Marks: 1

If the determinant of a matrix A is not equal to zero then the system of equations will have……….

Select correct option:

=>a unique solution

many solutions

infinite many solutions

None of the given choices

Question # 8 of 10 ( Start time: 11:21:37 PM ) Total Marks: 1

Sparse matrix is a matrix with ……….

Select correct option:

Some elements are zero

=>Many elements are zero

Some elements are one

Many elements are one

Question # 9 of 10 ( Start time: 11:22:12 PM ) Total Marks: 1

Which of the following is the meaning of partial pivoting while employing the row transformations?

Select correct option:

Making the largest element as pivot

Making the smallest element as pivot

Making any element as pivot

Making zero elements as pivot

Question # 10 of 10 ( Start time: 11:23:36 PM ) Total Marks: 1

If the Relaxation method is applied on the system; 2x+3y = 1, 3x +2y = - 4, then largest residual in 1st iteration will reduce to ---------.

Select correct option:

zero

4

-1

-1

4

Question # 1 of 10 ( Start time: 11:53:06 PM ) Total Marks: 1
Differences methods are iterative methods.

Select correct option:
TRUE
FALSE

Question # 2 of 10 ( Start time: 11:53:24 PM ) Total Marks: 1
A 3 x 3 identity matrix have three and different eigen values.

Select correct option:
TRUE
FALSE

Question # 3 of 10 ( Start time: 11:53:40 PM ) Total Marks: 1

Eigenvectors of a symmetric matrix are orthogonal, but only for distinct eigenvalues.

Select correct option:
TRUE
FALSE

Question # 4 of 10 ( Start time: 11:53:55 PM ) Total Marks: 1
The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the given 3 x 3 identity matrix. where symbol ^ shows power.

Select correct option:
(x-1)^3
(x+1)^3
x^3-1
x^3+1

Question # 5 of 10 ( Start time: 11:54:22 PM ) Total Marks: 1
The Power method can be used only to find the eigenvalue of A that is largest in absolute value—we call this eigenvalue the dominant eigenvalue of A.

Select correct option:
TRUE
FALSE

Question # 6 of 10 ( Start time: 11:54:39 PM ) Total Marks: 1
Below are all the finite difference methods EXCEPT _________.

Select correct option:
jacobi’s method
newton's backward difference method
Stirlling formula
Forward difference method

Question # 7 of 10 ( Start time: 11:55:15 PM ) Total Marks: 1
If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A.

Select correct option:
TRUE
FALSE

Question # 8 of 10 ( Start time: 11:55:28 PM ) Total Marks: 1
Eigenvalues of a _________ matrix are all real.

Select correct option:
symmetric
antisymmetric
rectangular
triangular

Question # 9 of 10 ( Start time: 11:55:53 PM ) Total Marks: 1
The determinant of a diagonal matrix is the product of the diagonal elements.

Select correct option:
TRUE
FALSE

Question # 10 of 10 ( Start time: 11:56:21 PM ) Total Marks: 1
The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.

Select correct option:
TRUE
FALSE

QUIZ.NO.3

Question # 1 of 10 ( Start time: 11:27:38 PM ) Total Marks: 1

While solving the system; x–2y = 1, x+4y = 4 by Gauss-Seidel method, which of the following ordering is feasible to have good approximate solution?

Select correct option:

x+4y = 1, x-2y = 4

x+2y = 1, x- 4y =4

x+4y = 4, x–2y = 1

no need to reordering

Question # 2 of 10 ( Start time: 11:28:58 PM ) Total Marks: 1

If the Relaxation method is applied on the system; 2x+3y = 1, 3x +2y = - 4, then largest residual in 1st iteration will reduce to ---------.

Select correct option:

zero

4

-1

-1

Question # 3 of 10 ( Start time: 11:30:01 PM ) Total Marks: 1

Which of the following rearrangement make strictly diagonal dominant, the system of linear equations; x-3y+z= –2, –6x+4y+11z=1, 5x–2y–2z=9?

Select correct option:

5x–2y–2z=9, x–3y+z= –2, –6x+4y+11z=1

–6x+4y+11z=1, x–3y+z= –2, 5x–2y–2z=9

5x–2y–2z=9, –6x+4y+11z=1, x–3y+z= –2

No need to rearrange as system is already in diagonal dominant form.

Question # 4 of 10 ( Start time: 11:31:21 PM ) Total Marks: 1

Back substitution procedure is used in …………….

Select correct option:

=>Gaussian Elimination Method

Jacobi’s method

Gauss-Seidel method

None of the given choices

Question # 5 of 10 ( Start time: 11:32:12 PM ) Total Marks: 1

The linear equation: 2x+0y-2=0 has -------- solution/solutions.

Select correct option:

=>unique

no solution

infinite many

finite many

Question # 6 of 10 ( Start time: 11:32:38 PM ) Total Marks: 1

If a system of equations has a property that each of the equation possesses one large coefficient and the larger coefficients in the equations correspond to different unknowns in different equations, then which of the following iterative method id preferred to apply?

Select correct option:

Gauss-Seidel method

Gauss-Jordon method

Gauss elimination method

Crout’s method

Question # 7 of 10 ( Start time: 11:34:03 PM ) Total Marks: 1

When the condition of diagonal dominance becomes true in Jacobi’s Method.Then its means that the method is …………….

Select correct option:

Stable

Unstable

Convergent

Divergent

Question # 8 of 10 ( Start time: 11:35:30 PM ) Total Marks: 1

For a system of linear equations, the corresponding coefficient matrix has the value of determinant; |A| = 0, then which of the following is true?

Select correct option:

The system has unique solution

The system has finite multiple solutions

The system has infinite may solutions

=>The system has no solution

Question # 9 of 10 ( Start time: 11:36:21 PM ) Total Marks: 1

For the system; 2x+3y = 1, 3x +2y = - 4, if the iterative solution is (0,0) and ‘dxi = 2’ is the increment in ‘y’ then which of the following will be taken as next iterative solution?

Select correct option:

(2,0)

(0,3)

(0,2)

(1,-4)

Question # 10 of 10 ( Start time: 11:37:49 PM ) Total Marks: 1

While using Relaxation method, which of the following is increment ‘dxi’corresponding to the largest Residual for 1st iteration on the system; 2x+3y = 1, 3x +2y = - 4 ?

Select correct option:

-2

2

3

4

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

QUIZ.NO.4

Question # 1 of 10 ( Start time: 11:40:42 PM)Total Marks: 1

If system of equations is inconsistent then its means that it has ………

Select correct option:

No Solutions

Many solutions

Infinite Many solutions

None of the given choices

Question # 2 of 10 ( Start time: 11:42:14 PM)Total Marks: 1

Which of the following method is not an iterative?

Select correct option:

Gauss–Seidel method

Iteration’s method

Relaxation Method

=>Gauss Jordan method

Question # 3 of 10 ( Start time: 11:43:46 PM)Total Marks: 1

Sparse matrix is a matrix with ……….

Select correct option:

Some elements are zero

=>Many elements are zero

Some elements are one

Many elements are one

Question # 4 of 10 ( Start time: 11:44:33 PM)Total Marks: 1

While using Relaxation method, which of the following is the Residuals for 1st iteration on the system; 2x+3y = 1, 3x +2y =4

Select correct option:

(2,3)

(3,-2)

(-2,3)

=>(1,4)

Question # 5 of 10 ( Start time: 11:46:06 PM)Total Marks: 1

The linear equation: 2x+0y-2=0 has -------- solution/solutions.

Select correct option:

unique

no solution

infinite many

finite many

Question # 6 of 10 ( Start time: 11:47:15 PM)Total Marks: 1

Relaxation Method is a/an ……….

Select correct option:

Direct method

=>Iterative method

Question # 7 of 10 ( Start time: 11:48:46 PM)Total Marks: 1

Gauss - Jordan Method is similar to ……….

Select correct option:

Gauss–Seidel method

Iteration’s method

Relaxation Method

Gaussian elimination method

Question # 8 of 10 ( Start time: 11:49:37 PM)Total Marks: 1

While using Relaxation method, which of the following is increment ‘dxi’corresponding to the largest Residual for 1st iteration on the system; 2x+3y = 1, 3x +2y = - 4 ?

Select correct option:

-2

2

3

4

Question # 9 of 10 ( Start time: 11:50:33 PM)Total Marks: 1

Full pivoting, in fact, is more ……………than the partial pivoting.

Select correct option:

Easiest

=>Complicated

Question # 10 of 10 ( Start time: 11:51:55 PM)Total Marks: 1

Gauss–Seidel method is also known as method of …………….

Select correct option:

Successive displacement

=>Iterations

False position

None of the given choices

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

QUIZ.NO.5

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Question # 2 of 10 ( Start time: 11:31:28 PM ) Total Marks: 1

Iterative algorithms can be more rapid than direct methods.

Select correct option:

FALSE

=>TRUE

Question # 3 of 10 ( Start time: 11:32:02 PM ) Total Marks: 1

Below are all the finite difference methods EXCEPT _________.

Select correct option:

jacobi’s method

newton's backward difference method

=>Stirlling formula

Forward difference method

Question # 4 of 10 ( Start time: 11:33:04 PM ) Total Marks: 1

Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.

Select correct option:

TRUE

FALSE

Question # 5 of 10 ( Start time: 11:33:36 PM ) Total Marks: 1

How many Eigen values will exist corresponding to the function; Exp(ax) = e^ax, when the matrix operator is of differentiation?

Select correct option:

Finite Multiple

Infinite many

Unique

None

Question # 6 of 10 ( Start time: 11:34:07 PM ) Total Marks: 1

Exact solution of 2/3 is not exists.

Select correct option:

=>TRUE

FALSE

Question # 7 of 10 ( Start time: 11:35:15 PM ) Total Marks: 1

The absolute value of a determinant (|detA|) is the product of the absolute values of the eigenvalues of matrix A

Select correct option:

TRUE

FALSE

Question # 8 of 10 ( Start time: 11:36:24 PM ) Total Marks: 1

By using determinants, we can easily check that the solution of the given system of linear equation ______ and it is ______.

Select correct option:

exits, unique

exists, consistent

trivial, unique

nontrivial, inconsistent

Question # 9 of 10 ( Start time: 11:36:46 PM ) Total Marks: 1

The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the matrix, remain …………… to the original vector.

Select correct option:

Perpendicular

Parallel

Diagonal

None of the given choices

Question # 10 of 10 ( Start time: 11:38:16 PM ) Total Marks: 1

In Jacobi’s method after finding D1, the sum of the diagonal elements of D1 should be ………… to the sum of the diagonal elements of the original matrix A.

Select correct option:

Greater than

Less than

Same

Different

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

QUIZ.NO.6

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Question # 1 of 10  Total Marks: 1

While solving by Gauss-Seidel method, which of the following is the first Iterative solution for the system; x-2y =1, x+4y=4 ?

Select correct option:

(1, 0.75)

(0,0)

(1,0)

(0,1)

Question # 2 of 10  Total Marks: 1

Sparse matrices arise in computing the numerical solution of …………….

Select correct option:

Ordinary differential equations

=>Partial differential equations

Linear differential equations

Non-linear differential equations

Question # 3 of 10  Total Marks: 1

While solving a system of linear equations by Gauss Jordon Method, after all the elementary row operations if there lefts also zeros on the main diagonal then which of the is true about the system?

Select correct option:

System may have unique solutions

System has no solution

System may have multiple numbers of finite solutions

System may have infinite many solutions

Question # 4 of 10  Total Marks: 1

Which of the following method is not an iterative method?

Select correct option:

Jacobi’s method

Gauss-Seidel method

Relaxation methods

Gauss-Jordan elimination method

Question # 5 of 10  Total Marks: 1

Numerical methods for finding the solution of the system of equations are classified as direct and ………… methods

Select correct option:

Indirect

Iterative

Jacobi

None of the given choices

Question # 6 of 10  Total Marks: 1

If the Relaxation method is applied on the system; 2x+3y = 1, 3x +2y = - 4, then largest residual in 1st iteration will reduce to -------.

Select correct option:

zero

4

-1

-1

Question # 7 of 10

Eigenvalues of a symmetric matrix are all _____ .

Select correct option:

=>real

complex

zero

positive

Question # 8 of 10

In the context of Jacobi’s method for finding Eigen values and Eigen vectors of a real symmetric matrix of order 2*2, if |-5| be its largest off-diagonal and its two equal diagonal values are ‘3’ then which of the following will be its corresponding argument value ‘theta’ of Orthogonal Matrix?

Select correct option:

Pi/3

Pi/6

Pi/2

Pi/4

Question # 9 of 10

If x is an eigen value corresponding to eigen value of V of a matrix A. If a is any constant, then x – a is an eigen value corresponding to eigen vector V is an of the matrix A - a I.

Select correct option:

=>TRUE

FALSE

Question # 10 of 10

An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to zero.

Select correct option:

TRUE

=>FALSE

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MC100401285 : Moaz Siddiq

Quiz Start Time: 10:31 PM
Time Left 86
sec(s)
Question # 1 of 10 ( Start time: 10:31:41 PM ) Total Marks: 1
Direct methods can be more rapid than iterative algorithms.
Select correct option:
TRUE
FALSE

MC100401285 : Moaz Siddiq

Quiz Start Time: 10:31 PM
Time Left 88
sec(s)
Question # 2 of 10 ( Start time: 10:32:18 PM ) Total Marks: 1
The dominant eigenvector of a matrix is an eigenvector corresponding to the eigenvalue of largest magnitude (for real numbers, smallest absolute value) of that matrix.
Select correct option:
TRUE
FALSE

MC100401285 : Moaz Siddiq

Quiz Start Time: 10:31 PM
Time Left 87
sec(s)
Question # 3 of 10 ( Start time: 10:32:43 PM ) Total Marks: 1
In the context of Jacobi’s method for finding Eigen values and Eigen vectors of a real symmetric matrix of order 2*2, if |-5| be its largest off-diagonal then which of the following will be its corresponding off- diagonal values of Orthogonal Matrix?
Select correct option:
Cos(theta), -Cos(theta)
Sin(theta), Cos(theta)
Sin(theta), -Sin(theta)
-Sin(theta), Cos(theta)

MC100401285 : Moaz Siddiq

Quiz Start Time: 10:31 PM
Time Left 87
sec(s)
Question # 4 of 10 ( Start time: 10:33:24 PM ) Total Marks: 1
The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.
Select correct option:
TRUE
FALSE

MC100401285 : Moaz Siddiq

Quiz Start Time: 10:31 PM
Time Left 84
sec(s)
Question # 5 of 10 ( Start time: 10:33:48 PM ) Total Marks: 1
The Jacobi iteration ______, if A is strictly diagonally dominant.
Select correct option:
converges
diverges

MC100401285 : Moaz Siddiq

Quiz Start Time: 10:31 PM
Time Left 89
sec(s)
Question # 6 of 10 ( Start time: 10:34:09 PM ) Total Marks: 1
For differences methods we require the set of values.
Select correct option:
TRUE
FALSE

MC100401285 : Moaz Siddiq

Quiz Start Time: 10:31 PM
Time Left 83
sec(s)
Question # 7 of 10 ( Start time: 10:34:25 PM ) Total Marks: 1
Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.
Select correct option:
TRUE
FALSE

MC100401285 : Moaz Siddiq

Quiz Start Time: 10:31 PM
Time Left 88
sec(s)
Question # 8 of 10 ( Start time: 10:35:24 PM ) Total Marks: 1
Let A be an n ×n matrix. The number x is an eigenvalue of A if there exists a non-zero vector v such that _______.
Select correct option:
Av = xv
Ax = xv
Av + xv=0
Av = Ax

MC100401285 : Moaz Siddiq

Quiz Start Time: 10:31 PM
Time Left 87
sec(s)
Question # 9 of 10 ( Start time: 10:35:56 PM ) Total Marks: 1
A 3 x 3 identity matrix have three and different eigen values.
Select correct option:
TRUE
FALSE

MC100401285 : Moaz Siddiq

Quiz Start Time: 10:31 PM
Time Left 87
sec(s)
Question # 10 of 10 ( Start time: 10:36:14 PM ) Total Marks: 1
The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the given 3 x 3 identity matrix. where symbol ^ shows power.
Select correct option:
(x-1)^3
(x+1)^3
x^3-1
x^3+1

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