GATE CH 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 14. Imported answers require independent review unless marked reviewed.

Topic practice 14 questionsPage 1 of 2

Which one of the following is the pair of eigenvalues of the matrix

Your answerChoose one option.

−7, 7

−5, 5

−4, 3

−3, 4

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Consider a Cartesian coordinate system defined over a 3-dimensional vector space with orthogonal unit basis vectors

and

. Let vector

, and vector

. The inner product of these vectors

Your answerChoose one option.

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Consider the matrix

The eigenvalues of the matrix are 0.27 and ____ (rounded off to 2 decimal places).

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Consider a linear homogeneous system of equations

, where

is an

matrix,

is an

vector and

is an

null vector. Let

be the rank of A. For a non-trivial solution to exist, which of the following conditions are/is satisfied?

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

Determinant of A = 0

Determinant of A ≠ 0

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Consider a matrix

, where

is a constant. If the eigenvalues of

are

and

, then the value of

, rounded off to the nearest integer, is __________

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If a matrix

is defined as

, the sum of all the eigenvalues of

is equal to ________ (in integer).

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Given matrix

, the ordered pair

for which

Your answerChoose one option.

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and

are vectors of length 4.

It is known that

is not a scalar multiple of

. Also,

is linearly independent of

and

. Further,

The rank of the matrix

is __________.

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Let

be a square matrix of size

(

). The elements of

are given by

The determinant of

Your answerChoose one option.

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For a matrix

, the diagonal elements are all zero and

. The minimum number of elements required to fully specify the matrix is _____.

Your answerChoose one option.

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GATE CH Linear Algebra PYQs

How to practice Linear Algebra

Question 23

Question 12

Question 45

Question 26

Question 30

Question 47

Question 12

Question 20

Question 26

Question 9