GATE AE 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 26. Imported answers require independent review unless marked reviewed.

Topic practice 26 questionsPage 1 of 3

square matrix

satisfies

. The determinant of this matrix may take which of the following value(s)?

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

−1

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

If a matrix can be written as

, where both

and

are

-dimensional real-valued non-zero column vectors, then the rank of the matrix A is ________ (answer in integer).

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

For the matrix

, if the relation

holds and

, then which one of the following statements about

is FALSE?

Your answerChoose one option.

is an eigenvector

is an eigenvalue

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

For any real symmetric matrix

, the transpose of

is ____ .

Your answerChoose one option.

inverse of

null matrix

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

The given system of equations has

Your answerChoose one option.

a unique solution.

infinitely many solutions.

no solution.

a finite number of solutions.

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

The eigenvalues of the matrix

are _____.

Your answerChoose one option.

0, 2

2, 3

1, 3

1, 2

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

The following system of linear equations

has:

Your answerChoose one option.

infinitely many solutions

a unique solution

no solution

three solutions

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

A particle acted upon by a constant force

N is displaced from point A with position vector

m to point B with position vector

m. The work done by this force is ______ J (answer in integer).

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

Consider the matrix

, where k is a constant. If the determinant of A is 3, then the ratio of the largest eigenvalue of A to the constant k is __________ (rounded off to 1 decimal place).

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

Which of the following statement(s) is/are true with respect to eigenvalues and eigenvectors of a matrix?

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

The sum of the eigenvalues of a matrix equals the sum of the elements of the principal diagonal.

is an eigenvalue of a matrix

, then

is always an eigenvalue of its transpose (

is an eigenvalue of an orthogonal matrix

, then

is also an eigenvalue of

If a matrix has

distinct eigenvalues, it also has

independent eigenvectors.

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

GATE AE Linear Algebra PYQs

How to practice Linear Algebra

Question 22

Question 32

Question 37

Question 11

Question 12

Question 13

Question 11

Question 30

Question 51

Question 29