GATE EE 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 27. Imported answers require independent review unless marked reviewed.

Topic practice 27 questionsPage 1 of 3

Two

matrices

and

have a common eigenvalue 2, and the same corresponding nonzero eigenvector.

Which of the following options is/are correct?

(Note:

is the

identity matrix.)

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

Determinant

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is an

skew-symmetric matrix with real-valued entries, and

is an

-dimensional column vector with real-valued entries such that

. The quantity

evaluates to ________

(Answer in integer)

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Which one of the following statements is ALWAYS correct about a collection of

column vectors, each having

real-valued entries?

Your answerChoose one option.

, then the column vectors must be linearly dependent

, then the column vectors must be linearly independent

, then the column vectors must be orthogonal

, then the column vectors must be linearly independent

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Consider an

orthogonal matrix

with real entries and each column having unit Euclidean norm.

Which of the following statements is/are correct?

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

The value of the determinant of

is either +1 or −1

The eigenvalues of

have modulus 1

, for all

, where

denotes the Euclidean norm of

, and

, for all distinct

, for all

, where

denotes the Euclidean norm of

, and

, for all

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Consider the system of linear equations:

, where

is an

matrix, and

and

are n-dimensional column vectors.

Suppose this system of equations has a unique solution. Which of the following statements is/are correct?

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

exists

The system of equations

also has a unique solution for

, for

, where

denotes the augmented matrix.

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Let

and

be the two eigenvectors corresponding to distinct eigenvalues of a

real symmetric matrix. Which one of the following statements is true?

Your answerChoose one option.

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Let

, and

. Then, the system of linear equations

has

Your answerChoose one option.

a unique solution.

infinitely many solutions.

a finite number of solutions.

no solution.

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Let

and let

be the identity matrix. Then

is equal to

Your answerChoose one option.

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Which one of the following matrices has an inverse?

Your answerChoose one option.

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The sum of the eigenvalues of the matrix

is ______ (rounded off to the nearest integer).

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GATE EE Linear Algebra PYQs

How to practice Linear Algebra

Question 30

Question 35

Question 49

Question 55

Question 56

Question 12

Question 13

Question 14

Question 11

Question 32