# 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
1. 1
2. 3
3. 2
4. 1

Question 2.

which of the following is true for two subspaces W1 & W2 of V(F)?
1. is the smallest subspace of V(F)
2. is the largest subspace of V(F)
3. is not a subspace of V(F)
4. all of the above

Question 3.

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

1. n – 1
2. 2n – 1
3. 2n2 – 1
4. 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?
1. The set of rows in A are LD
2. The system of equation AX = b is consistent for every 3. The system of equation AX = 0 has non-trivial solution
4. 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
1. 2
2. 3
3. 1
4. 4

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?
1. A skew-symmetric matrix of odd order is singular
2. Two similar matrices have the same minimal polynomial
3. A matrices B is nilpotent iff its trace is zero
4. 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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