GATE ES Linear Algebra PYQs & Answers

Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.

Questions 1–10 of 11. Imported answers require independent review unless marked reviewed.

Topic practice 11 questionsPage 1 of 2

, then

is ______.

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the matrix

. Which ONE of the following options CORRECTLY lists the eigenvalues of

Your answerChoose one option.

1; 8 −

; −8 +

2; 8 −

; −8 +

1; 8 +

; 8 −

2; 8 +

; 8 +

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A system of linear equations is given as

, where

, and

is the solution vector. Which of the following statements is/are TRUE for this system?

Your answerSelect all correct options. You can choose more than one.

Matrix

is skew-symmetric.

Eigenvalues of matrix

are real.

The system is homogeneous.

The system is singular.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The following is a system of linear equations

The value of

is __________. (rounded off to two decimal places)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The eigen values of the matrix

are

Your answerSelect all correct options. You can choose more than one.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

If X is a vector, and A and B are linear operators, then the correct mathematical relation(s) is/are

Your answerSelect all correct options. You can choose more than one.

(A+B)X = AX + BX

(λA)X = λ(AX)

(AB)X = A(BX)

(A+B)X = AᵀX+BᵀX

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

P and Q are square matrices. Consider the following

Y: Symmetric if

The correct choice is

Your answerChoose one option.

X is TRUE; Y is FALSE

X is FALSE; Y is TRUE

Both X and Y are TRUE

Both X and Y are FALSE

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider two matrices

and

. If

then det R is __________________ (in integer).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Given P is

matrix, Q is

matrix, R and S are

matrices, and superscript T denotes transpose. Consider

Relationship 1:

Relationship 2:

Which one of the following is correct?

Your answerChoose one option.

Relationship 1 is false; Relationship 2 is false

Relationship 1 is true; Relationship 2 is false

Relationship 1 is true; Relationship 2 is true

Relationship 1 is false; Relationship 2 is true

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Eigen values of the matrix

are

Your answerChoose one option.

1 and 2

1 and 3

1 and −2

0 and 3

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE ES Linear Algebra PYQs

How to practice Linear Algebra

Question 11

Question 37

Question 42

Question 48

Question 24

Question 25

Question 12

Question 48

Question 14

Question 37