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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.
Quadratic
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 = _{Ε}1/2+_{Ε}^{1/2}
δ = E^{1/2} −Ε^{1/2 }
Question : Muller’s method requires --------starting points
1
2
3
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 – 2^{ND} QUIZ FILE (24-11-2011)
EDIT BY MUHAMMAD AWAIS AND MUHAMMAD MOAAZ SIDDIQ
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?
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
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
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
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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