GATE CSE Linear Algebra PYQs & Answers — Page 2

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Questions 11–20 of 21. Imported answers require independent review unless marked reviewed.

Topic practice 21 questionsPage 2 of 3

Suppose that

is a

matrix such that every solution of the equation

is a scalar multiple of

. The rank of

is ________.

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For two

-dimensional real vectors

and

, the operation

is defined as follows:

Let

be a set of 10-dimensional non-zero real vectors such that for every pair of distinct vectors

. What is the maximum cardinality possible for the set

Your answerChoose one option.

100

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Consider the following matrix.

The largest eigenvalue of the above matrix is __________.

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Let

and

be two

matrices over real numbers. Let

and

denote the rank and determinant of a matrix

, respectively. Consider the following statements.

II.

III.

IV.

Which of the above statements are TRUE?

Your answerChoose one option.

I and II only

I and IV only

II and III only

III and IV only

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Let

be a square matrix. Consider the following two statements on

. I.

is invertible. II. Determinant of

is non-zero.

Which one of the following is TRUE?

Your answerChoose one option.

I implies II; II does not imply I.

II implies I; I does not imply II.

I does not imply II; II does not imply I.

I and II are equivalent statements.

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Consider the following matrix:

The absolute value of the product of Eigen values of R is ________.

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Let

be scalars, not all zero, such that

where

are column vectors in

. Consider the set of linear equations

where

and

. The set of equations has

Your answerChoose one option.

a unique solution at

where

denotes a

-dimensional vector of all 1

no solution

infinitely many solutions

finite many solutions

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Let

and

be two matrices. Then the rank of

is __________.

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Let

and

be two vectors in

whose Euclidean norms satisfy

. What is the value of

such that

bisects the angle between

and

Your answerChoose one option.

1/2

−1/2

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Let

be an

real valued square symmetric matrix of rank 2 with

. Consider the following statements.

(I) One eigenvalue must be in

(II) The eigenvalue with the largest magnitude must be strictly greater than 5

Which of the above statements about eigenvalues of

is/are necessarily CORRECT?

Your answerChoose one option.

Both (I) and (II)

(I) only

(II) only

Neither (I) nor (II)

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GATE CSE Linear Algebra PYQs

Question 24

Question 37

Question 52

Question 27

Question 9

Question 44

Question 3

Question 22

Question 30

Question 31