CSIR-NET Mathematical Science - Linear Algebra MCQ - Attempt Here!

By Astha Singh|Updated : June 23rd, 2022

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Multiple Choice Questions On Linear Algebra

Question 1.

Let A be a 4 × 4 matrix. Such that both A & Adj (A) are non-null matrices. It det A = 0 then the rank (A) is

Question 2.

which of the following is true for two subspaces W₁ & W₂ of V(F)?

is the smallest subspace of V(F)
is the largest subspace of V(F)
is not a subspace of V(F)
all of the above

Question 3.

Consider W = {(a₁, a₂, … a_n)|a₁ + 2a₂ + … + na_n = 0} is a subspace of then what is the dimension of W?

n – 1
2n – 1
2n² – 1
2n-2

Question 4.

Let A & B be two n × n matrices over a field F then

A. AB – BA = I, characteristic of F must be infinite

B. AB – BA = I, characteristic of F must be composite

C. AB – BA = I, characteristic of F always finite & non – zero

D. None of these.

Question 5.

Let A be a 4 × 3 matrix whose column forms a LI set then which of the following is/are false?

The set of rows in A are LD
The system of equation AX = b is consistent for every
The system of equation AX = 0 has non-trivial solution
there is a matrix B such that AB = I₄

Question 6.

For the following system of equations which of the following statements is not true?

A. the system of two equations in two unknown infinitely many solutions

B. Specifically

for any

will be the solution

C. This system of two equations in two unknowns has no solutions

D. This system of two equations in two unknowns inconsistent

Question 7.

If the characteristics polynomial of a matrix is

and the minimal polynomial is

then the number of all possible Jarden forms of the matrix is

Question 8.

Let M be a real

matrix which has 0, 1, and -1 as eigenvalues which of the following is true of M?

A. M⁸ + M⁴ = M⁶ + M²

^B.M + 3M² + 2M = M⁶ + 2M⁴ + 3M³

^C.M⁸ + 3M² + 2M = M⁶ + 2 M⁴ + 3M³

^D.M⁹ + 3M² + 2M = M⁶ + 2 M⁴ + 3M³

Question 9.

The rank and signature of the quadratic form -xy + z² in three variables over the reals is

A. (3,3)

B. (2,1)

C. (3,1)

D. (3,2)

Question 10.

Which of the following is/are true?

A skew-symmetric matrix of odd order is singular
Two similar matrices have the same minimal polynomial
A matrices B is nilpotent iff its trace is zero
If a matrix A is similar to a diagonal matrix, then A is similar to its transpose.

Answer Key For Linear Algebra
Question Number	Answer Key
1	B
2	D
3	C
4	D
5	B, C And D
6	C
7	A
8	A, B And D
9	C
10	A, B And D

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