GATE IN Linear Algebra PYQs & Answers — Page 2

Questions 11–20 of 23. Imported answers require independent review unless marked reviewed.

Topic practice 23 questionsPage 2 of 3

Consider the row vectors

and

. The rank of the matrix

, where the superscript

denotes the transpose, is

Your answerChoose one option.

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The determinant of the matrix M shown below is ____.

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Given

. The value of the determinant

___.

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The unit vectors along the mutually perpendicular

and

axes are

and

respectively. Consider the plane

and two vectors

and

on that plane such that

for any scalar

. A vector perpendicular to both

and

is ____.

Your answerChoose one option.

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A set of linear equations is given in the form

, where

is a

matrix with real number entries and

. Will it be possible to solve for

and obtain a unique solution by multiplying both left and right sides of the equation by

(the super script

denotes the transpose) and inverting the matrix

? Answer is ____.

Your answerChoose one option.

Yes, it is always possible to get a unique solution for any

matrix $A.

No, it is not possible to get a unique solution for any

matrix $A.

Yes, can obtain a unique solution provided the matrix

is well conditioned

Yes, can obtain a unique solution provided the matrix

is well conditioned

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Consider the matrix

. One of the eigenvectors of

Your answerChoose one option.

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are three orthogonal vectors. Given that

and

, the vector

is parallel to

Your answerChoose one option.

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A 3 × 3 matrix has eigenvalues 1, 2 and 5. The determinant of the matrix is ______.

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Let

be a 3 by 3 matrix with real number entries. The matrix

is such that

. The eigen values of N are

Your answerChoose one option.

0, 0, 0

0, 0, 1

0, 1, 1

1, 1, 1

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Consider the following system of linear equations:

Here

and

are the unknowns and

is a real constant. The value of

for which there are infinite number of solutions is

Your answerChoose one option.

−3

−6

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GATE IN Linear Algebra PYQs

Question 1

Question 25

Question 38

Question 1

Question 3

Question 26

Question 1

Question 16

Question 1

Question 28