GATE XE 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 18. Imported answers require independent review unless marked reviewed.

Topic practice 18 questionsPage 1 of 2

Consider the matrix

. Then, which of the following statements is/are true?

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

All the eigenvalues of

are real numbers

The eigenvalues of

are

The determinant of

is 3

The matrix

is invertible, where

denotes the identity matrix of order

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Let

be the LU decomposition of the matrix

Then, the value of

(in integer) is ________.

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Suppose that 2 is an eigenvalue of the matrix

Then the value of

is equal to (Answer in integer)

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For

, consider the system of linear equations

If the system has infinitely many solutions, then which of the following statements is/are correct?

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

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Let

be a

matrix whose eigenvalues are 2, 3, 4 and let

be the identity matrix of order 3. If

for some integer

, then the value of

is _____

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Let

and

be two square matrices of the same order. Then, which of the following matrices is/are necessarily equal to

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

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Let

be a

real matrix having eigenvalues 1, 2 and 3. If

, where

is the

identity matrix, then the eigenvalues of

are

Your answerChoose one option.

4, 9, 16

1, 2, 3

1, 4, 9

4, 16, 25

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Let

The eigenvalues of both

and

are 1, 1, and 2. Which one of the following statements is TRUE?

Your answerChoose one option.

Both

and

are diagonalizable

is diagonalizable but

is NOT diagonalizable

is NOT diagonalizable but

is diagonalizable

Both

and

are NOT diagonalizable

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Let

. Then the sum of the geometric multiplicities of the distinct eigenvalues of

is equal to ______.

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Let

and

matrices with real entries. Consider the following statements:

P: If

is symmetric then

Number of nonzero eigen values (count multiplicity) of

Q: If

then

Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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GATE XE Linear Algebra PYQs

How to practice Linear Algebra

Question 15

Question 20

Question 17

Question 20

Question 15

Question 19

Question 11

Question 18

Question 16

Question 19