GATE ME topic:linear-algebra PYQs & Answers

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topic:linear-algebra

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Questions 1–10 of 23. Imported answers require independent review unless marked reviewed.

Topic practice 23 questionsPage 1 of 3

Let A and B be real symmetric matrices of same size. Which one of the following options is correct?

Your answerChoose one option.

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Consider the system of linear equations

The values of

and

such that there exists a non-trivial null space and the system admits infinite solutions are

Your answerChoose one option.

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The matrix

(where

) has a negative eigenvalue if

is greater than

Your answerChoose one option.

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A linear transformation maps a point

in the plane to the point

according to the rule

Then, the disc

gets transformed to a region with an area equal to ________ . (Rounded off to two decimals)

Use π = 3.14.

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is a symmetric matrix, the value of

is ____________.

Your answerChoose one option.

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The system of linear equations in real

given by

involves a real parameter

and has infinitely many non-trivial solutions for special value(s) of

. Which one or more among the following options is/are non-trivial solution(s) of

for such special value(s) of

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

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A is a

real matrix of rank 2. For the set of homogeneous equations

, where

is a zero vector and

is a vector of unknown variables, which of the following is/are true?

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

The given set of equations will have a unique solution.

The given set of equations will be satisfied by a zero vector of appropriate size.

The given set of equations will have infinitely many solutions.

The given set of equations will have many but a finite number of solutions.

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If the sum and product of eigenvalues of a

real matrix

are 4 and

respectively, then

is _____ (in integer).

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Consider an

matrix

and a non-zero

vector

. Their product

, where

and

. Based on the given information, the eigen value of

is:

Your answerChoose one option.

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Consider a vector

in 2-dimensional space. Let its direction (counter-clockwise angle with the positive

-axis) be

. Let

be an eigenvector of a

matrix

with corresponding eigenvalue

. If we denote the magnitude of a vector

, identify the VALID statement regarding

, where

Your answerChoose one option.

Direction of

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GATE ME topic:linear-algebra PYQs

How to practice topic:linear-algebra

Question 11

Question 14

Question 36

Question 32

Question 15

Question 46

Question 46

Question 48

Question 1

Question 26