GATE MA topic:linear-algebra PYQs & Answers — Page 4

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topic:linear-algebra

Questions 31–40 of 62. Imported answers require independent review unless marked reviewed.

Topic practice 62 questionsPage 4 of 7

Consider

P: Let

with

. If

, then the system of linear equations

has

as the only solution.

Q: Let

be a non-zero matrix such that

. Then

is a singular matrix.

Which of the following statements is TRUE?

Your answerChoose one option.

Both P and Q are TRUE

Both P and Q are FALSE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

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Let

be a linear transformation defined by

For

, let

. Which of the following statements is TRUE?

Your answerChoose one option.

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Consider

as a vector space with the usual operations of vector addition and scalar multiplication. Let

be denoted by

. Define subspaces

and

Let

denote the dimension of the subspace

Which of the following statements are TRUE?

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

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Let

be a

real matrix such that

. If the determinant of

, then the trace of

equals _____.

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Let

be a

matrix and

be a

matrix with real entries such that

is non-singular. Consider the following statements:

P: Nullity of

is 0.

is a non-singular matrix.

Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Let

be the row reduced echelon form of a

real matrix

and let the third column of

. Consider the following statements:

P: If

is a solution of

, then

Q: For all

Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Let

be a linear transformation such that

, and

. Then the rank of

is _____.

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Let

be an inner product on the vector space

over

. Consider the following statements: P:

for all

. Q: If

for all

, then

. Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Let

be a square matrix such that

, where

denotes the determinant of a square matrix

. If

, then the geometric multiplicity of the eigenvalue

is __________.

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Let

be the vector space of all polynomials of degree at most 2 over the real field

. Let

be the linear operator given by

Then the sum of the eigenvalues of

is __________.

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GATE MA topic:linear-algebra PYQs

Question 12

Question 47

Question 56

Question 65

Question 1

Question 4

Question 19

Question 43

Question 49

Question 52