GATE EE Linear Algebra PYQs & Answers — Page 2

Questions 11–20 of 27. Imported answers require independent review unless marked reviewed.

Topic practice 27 questionsPage 2 of 3

For a given vector

, the vector normal to the plane defined by

Your answerChoose one option.

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In the figure, the vectors u and v are related as: Au = v by a transformation matrix A. The correct choice of A is

Diagram for Electrical Engineering question 24

Your answerChoose one option.

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Consider a 3 x 3 matrix

whose

-th element,

. Then the matrix

will be

Your answerChoose one option.

symmetric.

skew-symmetric.

unitary.

null.

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denotes the exponential of a square matrix

. Suppose

is an eigenvalue and

is the corresponding eigen-vector of matrix

. Consider the following two statements: Statement 1:

is an eigenvalue of

. Statement 2:

is an eigen-vector of

. Which one of the following options is correct?

Your answerChoose one option.

Statement 1 is true and statement 2 is false.

Statement 1 is false and statement 2 is true.

Both the statements are correct.

Both the statements are false.

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Consider a matrix

. The matrix

satisfies the equation

, where

and

are scalars and

is the identity matrix. Then

is equal to

Your answerChoose one option.

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Let

and

be real numbers such that

. The eigenvalues of the matrix

are

Your answerChoose one option.

1 and 1

1 and -1

j and -j

pq and -pq

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Let A be a

matrix such that

is a null matrix, and let I be the

identity matrix. The determinant of

is _____________.

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is a polynomial on real

over real coefficients

where

. Which of the following statements is true?

Your answerChoose one option.

can be chosen to ensure that

is a root for any given set

No choice of coefficients can make all roots identical.

can be chosen to ensure that all roots are complex.

alone cannot ensure that all roots are real.

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The number of purely real elements in a lower triangular representation of the given

matrix, obtained through the given decomposition is ________.

Your answerChoose one option.

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is a

matrix with eigenvalues 4 and 9. The eigenvalues of

are

Your answerChoose one option.

4 and 9

2 and 3

-2 and -3

16 and 81

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GATE EE Linear Algebra PYQs

Question 11

Question 24

Question 20

Question 40

Question 42

Question 1

Question 38

Question 1

Question 42

Question 2