GATE MT 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 12. Imported answers require independent review unless marked reviewed.

Topic practice 12 questionsPage 1 of 2

Select the correct pair of eigen vectors for the following symmetric matrix

Your answerChoose one option.

and

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Which one of the following matrices has eigenvalues 1 and 6?

Your answerChoose one option.

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Which one of the following matrices is orthogonal?

Your answerChoose one option.

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Which of the following statements is/are correct for a square matrix

with real number entries?

denotes the transpose of

and

denotes the inverse of

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

is symmetric if

is skew-symmetric if

is orthogonal, then

is orthogonal, then its determinant is zero.

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, where

are not identically zero, then the values of

are

Your answerChoose one option.

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The sum of eigen values of the matrix

is __________ (in integer).

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For the equation

the value of

is __________ (in integer).

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For a

matrix, the value of the determinant is −48 and the trace is 8. If one of the eigenvalues is 4, the other two are ________

Your answerChoose one option.

2, −3

1, −3

6, −2

−4, 0

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For the matrix given below, the eigenvalues are:

Your answerChoose one option.

0, 2, 2

1, 1, 2

0, 1, 2

0, 1, 3

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M and N are

matrices. If the det(M) is −9 and the det(N) is −14, then the det(NM) is ______ (round off to the nearest integer).

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GATE MT Linear Algebra PYQs

How to practice Linear Algebra

Question 12

Question 11

Question 41

Question 28

Question 36

Question 30

Question 54

Question 42

Question 1

Question 55