GATE DA topic:linear-algebra PYQs & Answers — Page 2

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topic:linear-algebra

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

Topic practice 21 questionsPage 2 of 3

Let

be such that

. Which one of the following statements is ALWAYS correct?

Your answerChoose one option.

is invertible

Determinant of

is 0

The sum of the diagonal elements of

is 1

and

have the same rank

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Let

be a set of linearly independent vectors in

. Let the

-th element of matrix

be given by

. Which one of the following statements is correct?

Your answerChoose one option.

is invertible

0 is a singular value of

Determinant of

is 0

for some non-zero

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Let

be a system of orthonormal vectors in

. Consider the matrix

. Which of the following statements is/are correct?

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

Singular values of

are also its eigenvalues

Singular values of

are either 0 or 1

Determinant of

is 1

is invertible

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matrix

with real entries satisfies the property:

, for all

, where

denotes the Euclidean norm. Which of the following statements is/are ALWAYS correct?

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

must be orthogonal

, where

denotes the identity matrix, is the only solution

The eigenvalues of

are either

has full rank

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Let

be a dataset of

observations where each

. It is given that

. The covariance matrix computed from

has eigenvalues

. Let

be the direction of maximum variance with

The value of

(Answer in integer)

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Consider the matrix

Which ONE of the following statements is TRUE?

Your answerChoose one option.

The eigenvalues of

are non-negative and real.

The eigenvalues of

are complex conjugate pairs.

One eigenvalue of

is positive and real, and another eigenvalue of

is zero.

One eigenvalue of

is non-negative and real, and another eigenvalue of

is negative and real.

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Consider the

matrix

The determinant of

is _____.

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Select all choices that are subspaces of

Note:

denotes the set of real numbers.

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

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Which of the following statements is/are TRUE?

Note:

denotes the set of real numbers.

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

There exist

, and

such that

has a unique solution and

has infinite solutions.

There exist

, and

such that

has no solutions and

has infinite solutions.

There exist

, and

such that

has a unique solution and

has infinite solutions.

There exist

, and

such that

has a unique solution and

has no solutions.

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Let

be the set of real numbers,

be a subspace of

and

be the matrix corresponding to the projection onto the subspace

. Which of the following statements is/are TRUE?

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

is a 1-dimensional subspace of

, then the null space of

is a 1-dimensional subspace.

is a 2-dimensional subspace of

, then the null space of

is a 1-dimensional subspace.

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GATE DA topic:linear-algebra PYQs

Question 37

Question 38

Question 50

Question 52

Question 60

Question 13

Question 35

Question 47

Question 48

Question 49