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# MTH501 Linear Algebra Solved MCQs Final Term Papers Mega File

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For any subspace W of a vector space V, which one is not the axiom for subspace.

0 must be in W.

For all u, v in W and u – v must be in W.

For all u, v in W and u.v must be in W.

For any scalar k and u in W then k.u in W.

Which one is not the axiom for vector space?

0 + u = u

0.u = u

1.u = u

u + v = v + u

The Gauss-Seidel method is applicable to strictly diagonally dominant matrix.

TRUE

FALSE

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

At what condition det(AB)=(detA)(detB) is possible?

When A and B are n x n matrices

When A is a row matrix

When A and B are m x n matrices

When B is a column matrix

For any 3x3 matrix A where det (A) = 3, then det (2A) = ________.

24

20

15

6

If a multiple of one row of a square matrix A is added to another row to produce a matrix B, then which of the following condition is true?

detB = detA

detB = k detA

detA detB = 0

detA detB = detA

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

TRUE

FALSE

While using the Cramer’s rule, if determinant D = 0, and other determinant is not zero then how many solutions are there?

Many solutions

No solution

Two solutions

One solution

Which of the following is all permutations of {1,2}?

(1,2,2,1)

Question # 1 of 10 ( Start time: 09:52:17 PM ) Total Marks: 1
By using determinants, we can easily check that the solution of the given system of linear equation exits and it is unique.
Select correct option:

FALSE
TRUE

Question # 2 of 10 ( Start time: 09:53:11 PM ) Total Marks: 1
If a multiple of one row of a square matrix A is added to another row to produce a matrix B, then which of the following condition is true?
Select correct option:

detB = k detA
detB = detA
detA detB = 0
detA detB = detA

Question # 3 of 10 ( Start time: 09:54:09 PM ) Total Marks: 1
At what condition the Cramer’s formula is valid for linear systems?
Select correct option:

When matrix is n x n
When det(A) is equal to zero
When matrix is m x n
When det(A) in not equal to zero

Question # 4 of 10 ( Start time: 09:54:44 PM ) Total Marks: 1
A matrix has not the same determinant if we add a multiple of a column to another column.
Select correct option:

TRUE
FALSE

Question # 5 of 10 ( Start time: 09:55:30 PM ) Total Marks: 1
The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal.
Select correct option:

TRUE
FALSE

Question # 6 of 10 ( Start time: 09:56:10 PM ) Total Marks: 1
Which of the following is the volume of the parallelepiped determined by the columns of A where A is a 3 x 3 matrix?
Select correct option:

|det A|
[A]
det A
A^(-1) ,that is inverse of A

Question # 7 of 10 ( Start time: 09:57:25 PM ) Total Marks: 1
For any 3x3 matrix A where det (A) = 3, then det (2A) = ________.
Select correct option:

24
20
15
6

Question # 8 of 10 ( Start time: 09:58:24 PM ) Total Marks: 1
Which one is not the axiom for vector space?
Select correct option:

0 + u = u
0.u = u
1.u = u
u + v = v + u

2

Question # 9 of 10 ( Start time: 09:58:58 PM ) Total Marks: 1
Which of the following is NOT the axiom for vector space where u, v, w in V are set of vectors and l, m, n are scalars?
Select correct option:

u + (v + w) = (u + v) + w
u.v =v.u
l (u + v)= l u + l v
(l +m) u= I u+ m u

Question # 10 of 10 ( Start time: 09:59:48 PM ) Total Marks: 1
If two rows or columns of a square matrix are identical, then det (A)wil be _______.
Select correct option:

zero
non zero
one
positive

Question # 1 of 10 ( Start time: 10:30:38 PM ) Total Marks: 1
If A is strictly diagonally dominant, then A is _________.
Select correct option:

invertible
singular
symmetric
scalar

Question # 2 of 10 ( Start time: 10:31:17 PM ) Total Marks: 1
The Gauss-Seidel method is applicable to strictly diagonally dominant matrix.
Select correct option:

TRUE
FALSE

Question # 3 of 10 ( Start time: 10:32:00 PM ) Total Marks: 1
If the absolute value of each diagonal entry exceeds the sum of the absolute values of the other entries in the same row then a matrix A is called:
Select correct option:

invertible
strictly diagonally dominant
diagonally
scalar

Question # 4 of 10 ( Start time: 10:33:26 PM ) Total Marks: 1
The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal.
Select correct option:

TRUE
FALSE

Question # 5 of 10 ( Start time: 10:33:52 PM ) Total Marks: 1
Which one is not the axiom for vector space?
Select correct option:

0 + u = u
0.u = u
1.u = u
u + v = v + u

Question # 6 of 10 ( Start time: 10:34:16 PM ) Total Marks: 1
Let W = {(x, y) such that x, y in R and x = y}. Is W a vector subspace of plane.
Select correct option:

YES
NO

Question # 7 of 10 ( Start time: 10:34:58 PM ) Total Marks: 1
If A is a triangular matrix, then det(A) is the product of the entries on the ________.
Select correct option:

main diagonal of A
first two rows of A
diagonal of A
first two columns of A

Question # 8 of 10 ( Start time: 10:35:59 PM ) Total Marks: 1
By using determinants, we can easily check that the solution of the given system of linear equation exits and it is unique.
Select correct option:

FALSE
TRUE

Question # 9 of 10 ( Start time: 10:36:55 PM ) Total Marks: 1
If a matrix A is invertible than adj(A) is also invertible.
Select correct option:

TRUE
FALSE

Question # 10 of 10 ( Start time: 10:37:57 PM ) Total Marks: 1
If all the entries of a row or a column of a square matrix are zero, then det (A) will be _____________.
Select correct option:

zero
infinity
one
non zero

Quiz Start Time: 08:32 PM

 Time Left 57 sec(s)

Question # 3 of 10 ( Start time: 08:34:27 PM )

Total Marks: 1

A matrix A and its transpose have the same determinant.

Select correct option:

Bottom of Form

Top of Form

Quiz Start Time: 08:32 PM

 Time Left 48 sec(s)

Question # 5 of 10 ( Start time: 08:36:08 PM )

Total Marks: 1

If a system of equations is solved using the Jacobi’s method , then which of the following is the most appropriate answer about the matrix M that is derived from the coefficient matrix ?

Select correct option:

Bottom of Form

Top of Form

Quiz Start Time: 08:32 PM

 Time Left 66 sec(s)

Question # 6 of 10 ( Start time: 08:37:37 PM )

Total Marks: 1

If A is a square matrix, then the Minor of entry ith row and jth column is to be the determinant of the sub matrix that remains when the ith row and jth column of A are:

Select correct option:

Bottom of Form

Top of Form

Quiz Start Time: 08:32 PM

 Time Left 36 sec(s)

Question # 7 of 10 ( Start time: 08:38:54 PM )

Total Marks: 1

If M=[3] then which of the following is the determinant of the matrix M?

Select correct option:

Bottom of Form

For which of the matrix, the Gauss-Seidel method is applicable

Top of Form

Quiz Start Time: 08:32 PM

 Time Left 71 sec(s)

Question # 9 of 10 ( Start time: 08:41:21 PM )

Total Marks: 1

Which of the following is all permutations of {1,2}?

Select correct option:

Top of Form

Quiz Start Time: 08:32 PM

 Time Left 56 sec(s)

Question # 10 of 10 ( Start time: 08:42:29 PM )

Total Marks: 1

If M is a square matrix having two rows equal then which of the following about the determinant of the matrix is true?

Select correct option:

Quiz Start Time: 05:46 PM

 Time Left 37 sec(s)

Question # 1 of 10 ( Start time: 05:46:20 PM )

If a system of equations is solved using the Gauss-Seidel method, then which of the following is the most appropriate answer about the matrix M that is derived from the coefficient matrix ?

Select correct option:

 true

Bottom of Form

Top of Form

Quiz Start Time: 05:46 PM

 Time Left 81 sec(s)

Question # 3 of 10 ( Start time: 05:48:07 PM )

Let W = {(1, y) such that y in R}. Is W a vector subspace of plane.

Select correct option:

 true

Quiz Start Time: 05:46 PM

 Time Left 89 sec(s)

Question # 4 of 10 ( Start time: 05:48:39 PM )

Which of the following is the volume of the parallelepiped determined by the columns of A where A is a 3 x 3 matrix?

Select correct option:

 true

Bottom of Form

Top of Form

Quiz Start Time: 05:46 PM

 Time Left 89 sec(s)

Question # 5 of 10 ( Start time: 05:50:05 PM )

At what condition the Cramer’s rule fails?

Select correct option:

 true

Bottom of Form

Top of Form

Quiz Start Time: 05:46 PM

 Time Left 74 sec(s)

Question # 6 of 10 ( Start time: 05:50:21 PM )

All the lines those passes through origin are not the subspace of a plane.

Select correct option:

 true

Bottom of Form

Top of Form

Quiz Start Time: 05:46 PM

 Time Left 79 sec(s)

Question # 7 of 10 ( Start time: 05:50:55 PM )

A matrix A and its transpose have the same determinant.

Select correct option:

 true

Bottom of Form

Top of Form

Quiz Start Time: 05:46 PM

 Time Left 83 sec(s)

Question # 8 of 10 ( Start time: 05:51:08 PM )

Cramer’s rule is a formula for solving systems of equations by __________.

Select correct option:

 true

Bottom of Form

Top of Form

Quiz Start Time: 05:46 PM

 Time Left 83 sec(s)

Question # 9 of 10 ( Start time: 05:51:30 PM )

If a system of equations is solved using the Jacobi’s method , then which of the following is the most appropriate answer about the matrix M that is derived from the coefficient matrix ?

Select correct option:

Bottom of Form

Top of Form

Quiz Start Time: 05:46 PM

 Time Left 87 sec(s)

Question # 10 of 10 ( Start time: 05:52:59 PM )

Which of the following is all permutations of {1,2}?

Select correct option:

 true

Consider a system of linear equations A x =b where A is a3 ×3  matrix having 3 pivot positions, then which

statement is false about the system Ax =b

(a)  System has unique solution.

(b)  Rank of the matrix is 3.

(c)  There is only one free variable in solution of that system.

(d)  The associated homogeneous system Ax =0 has only trivial system.

If a finite set S of non zero vectors span a vector space V, then some subset of S is a basis for V.

1.  True

2.  false

D

If rank of a3 x 5 matrix  is 3 then dimension of its Null space is

(a)  0

(b)  3

(c)  2

(d)  We can’t say anything

1

If matrix A has zero as an eigenvalue then which statement(s) about A must be true.

I.  Matrix A is not invertible.

II.  Matrix A will also have an eigenvalue 2.

III.  Matrix is diagonalizable.

1  II and III only.

2 I only.    (true)

3  II and III only.

4  All three.

• 1
• 2
• 0
• 3

1 x 3

3 x 1

3 x 3

4 x 1

Determinant of  a non-invertible(singular) matrix always

► vanish

►  unity

►  non zero negative

► non zero positive

Rank of  a zero matrix of any order is

► zero

► three

► four

► nine

► Zero

► One

► Two

► Three

Are orthogonal

►Having their inner product zero

► Can span a subspace while both passing through the origin

► All above statements are equivalent

► Infinite many solutions

►  Empty solution

►  Unique, non-trivial solution

►  Unique, trivial solution

► Not defined

►One

► Zero

►  Arbitrary

► 4

► 2

► 1

► Inconclusive

► Infinite many solutions

►  Empty solution

►  Unique, non-trivial solution

►  Unique, trivial solution

Question No: 1    ( Marks: 2 )     -  Please choose one

The characteristics polynomial for the matrix  A= is

 ► ► ► ►

Question No: 2    ( Marks: 2 )     -  Please choose one

Let A=PA then what will be where A= , D=

 ► ► ► ► None of the other

Question No: 3    ( Marks: 2 )     -  Please choose one

The origin of the dynamical system =A for the matrix A=  is

 ► Attractor ► Repellor ► Saddle point ► None of them

Question No: 4    ( Marks: 2 )     -  Please choose one

The distance between the vectors  u=(7,1) and v=(3,2)is

 ► ► ► ►

Question No: 5    ( Marks: 2 )     -  Please choose one

The vectors  ,  ,  are

 ► Parallel ► Orthogonal ► Not  Orthogonal ► Not parallel

Question No: 1      ( Marks: 1 ) - Please choose one

Reduced echelon form of the matrix is

►

►

►

Dear sir!

kindly convert this file in simple Ms.word or in PDF format

thanks

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