GATE ECE topic:linear-algebra PYQs & Answers

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topic:linear-algebra

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Questions 1–10 of 21. Imported answers require independent review unless marked reviewed.

Topic practice 21 questionsPage 1 of 3

Consider the matrix

. Which of the following options is/are TRUE if

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

and

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Consider the matrix

below:

For which of the following combinations of

and

, is the rank of

at least three?

(i)

and

(ii)

(iii)

and

(iv)

Your answerChoose one option.

Only (i), (iii), and (iv)

Only (iv)

Only (ii)

Only (i) and (iii)

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Consider the vectors

For real-valued scalar variable

, the value of

is __________ (rounded off to two decimal places).

denotes the Euclidean norm, i.e., for

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Let

and

denote the set of real numbers and the three dimensional vector space over it, respectively. The value of

for which the set of vectors

does not form a basis of

is ______.

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Consider the matrix

, where

is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix?

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

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Let

and

be two vectors. The value of the coefficient

in the expression

, which minimizes the length of the error vector

, is

Your answerChoose one option.

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Let the sets of eigenvalues and eigenvectors of a matrix

and

, respectively. For any invertible matrix

, the sets of eigenvalues and eigenvectors of the matrix

, where

, respectively, are

Your answerChoose one option.

and

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Let

be an

real column vector with length

. The trace of the matrix

Your answerChoose one option.

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Consider a system of linear equations

, where

This system of equations admits ________.

Your answerChoose one option.

a unique solution for

infinitely many solutions for

no solutions for

exactly two solutions for

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Let

be two non-zero real numbers and

be two non-zero real vectors of size

. Suppose that

and

satisfy

, and

. Let

be the

matrix given by:

The eigenvalues of

are ________.

Your answerChoose one option.

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GATE ECE topic:linear-algebra PYQs

How to practice topic:linear-algebra

Question 26

Question 11

Question 59

Question 30

Question 55

Question 11

Question 15

Question 38

Question 12

Question 37