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

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topic:linear-algebra

Questions 11–20 of 39. Imported answers require independent review unless marked reviewed.

Topic practice 39 questionsPage 2 of 4

The statements P and Q are related to matrices A and B, which are conformable for both addition and multiplication.

Which one of the following options is CORRECT?

Your answerChoose one option.

P is TRUE and Q is FALSE

Both P and Q are TRUE

P is FALSE and Q is TRUE

Both P and Q are FALSE

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What are the eigenvalues of the matrix

Your answerChoose one option.

1, 2, 5

1, 3, 4

−5, 1, 2

−5, −1, 2

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Consider two matrices

and

The determinant of the matrix

is __________ (in integer).

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is an arbitrary real

matrix, then which of the following matrices will have non-negative eigenvalues?

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

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For the matrix

which of the following statements is/are TRUE?

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

[A] = has a unique solution

[A] = does not have a unique solution

[A] has three linearly independent eigenvectors

[A] is a positive definite matrix

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Two vectors

and

belong to the null space of a 4 × 4 matrix of rank 2. Which one of the following vectors also belongs to the null space?

Your answerChoose one option.

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Cholesky decomposition is carried out on the following square matrix

Let

and

be the (i,j)

elements of matrices

and

, respectively. If the element

of the decomposed lower triangular matrix

is 1.968, what is the value (rounded off to the nearest integer) of the element

Your answerChoose one option.

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For the matrix

which of the following statements is/are TRUE?

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

The eigenvalues of

are same as the eigenvalues of

The eigenvalues of

are the reciprocals of the eigenvalues of

The eigenvectors of

are same as the eigenvectors of

The eigenvectors of

are same as the eigenvectors of

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The matrix

is defined as

and has eigenvalues 5 and −2. The matrix

is formed as

Which of the following is/are the eigenvalue(s) of matrix

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

−20

−30

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and

are two square matrices of the same order. Which of the following statement(s) is/are correct?

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

and

are invertible, then

and

are invertible, then

and

are invertible, then

and

are not invertible, then

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GATE CE topic:linear-algebra PYQs

Question 12

Question 36

Question 48

Question 24

Question 25

Question 37

Question 38

Question 47

Question 25

Question 25