GATE PI 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 13. Imported answers require independent review unless marked reviewed.

Topic practice 13 questionsPage 1 of 2

Which ONE of the following options CORRECTLY matches the matrices to their properties?

Matrix P =

; Q =

; R =

; S =

Properties: 1 Singular; 2 Triangular; 3 Symmetric; 4 Trace free.

Your answerChoose one option.

P-3; Q-1; R-4; S-2

P-4; Q-1; R-3; S-2

P-3; Q-4; R-1; S-2

P-4; Q-1; R-2; S-3

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The eigenvalues of the matrix

are

Your answerChoose one option.

and

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is a matrix such that

, where

is an identity matrix, then which of the following is TRUE?

Your answerChoose one option.

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Given matrices

and

; B is skew-symmetric matrix of A.

Your answerChoose one option.

−3

−2

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For the matrix

, eigenvalue corresponding to the eigenvector

is _____ (in integer).

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If a, b and c are the three vectors, the vector triple product

is given by

Your answerChoose one option.

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Matrix A as a product of two other matrices is given by

The value of det(A) is ____________. [round off to nearest integer]

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If a matrix is squared, then

Your answerChoose one option.

both eigenvalues and eigenvectors must change

both eigenvalues and eigenvectors are retained

eigenvalues get squared but eigenvectors are retained

eigenvalues are retained but eigenvectors change

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The eigenvalues of matrix

are 5 and 10. For matrix

, where

is a constant and

is a 2×2 identity matrix, its eigenvalues are

Your answerChoose one option.

5, 10

5 + α, 10 + α

5 - α, 10 - α

5α, 10α

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For the matrix

, the eigenvectors are

Your answerChoose one option.

and

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GATE PI Linear Algebra PYQs

How to practice Linear Algebra

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Question 11

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Question 36

Question 31

Question 27