GATE MA Linear Algebra PYQs & Answers — Page 3

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Questions 21–30 of 62. Imported answers require independent review unless marked reviewed.

Topic practice 62 questionsPage 3 of 7

Let

be the subset of

consisting of all

such that

for all

. The number of elements in

is equal to

(answer in integer)

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Let

be a linear transformation satisfying

and

. Then

Your answerChoose one option.

is one-one but

is NOT onto

is one-one and onto

is NEITHER one-one NOR onto

is NOT one-one but

is onto

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Let

. Consider the following statements:

is diagonalizable.

is diagonalizable. Which of the following statements is correct?

Your answerChoose one option.

is TRUE and

is FALSE

is FALSE and

is TRUE

Both

and

are FALSE

Both

and

are TRUE

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Let

be a linear transformation and the null space of

be the subspace of

given by

, where

is the identity map on

, then the minimal polynomial of

Your answerChoose one option.

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Consider

with the inner product

, for

and

. Let

and

denote the orthogonal complement of

. The dimension of

is equal to ______.

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Let

and

. If

for some

, then the value of

is equal to __________.

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Consider the linear system

, where

and

. Suppose

, where

and

are lower triangular and upper triangular square matrices, respectively. Consider the following statements:

: If each element of the main diagonal of

is 1, then

: For any choice of the initial vector

, the Jacobi iterates

converge to the unique solution of the linear system

Then

Your answerChoose one option.

both

and

are TRUE

is FALSE and

is TRUE

is TRUE and

is FALSE

both

and

are FALSE

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Let

be a

real matrix with

, where

and

is the

identity matrix. If

, then the trace of

is __________.

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Let

be a

real matrix such that

is the degree of the minimal polynomial of

, then

equals __________.

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Suppose that the characteristic equation of

where

with

. Which of the following statements is TRUE?

Your answerChoose one option.

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GATE MA Linear Algebra PYQs

Question 60

Question 14

Question 19

Question 22

Question 34

Question 35

Question 40

Question 59

Question 60

Question 11