GATE EE 2023 | Linear Algebra Question 13 | Engineering Mathematics | GATE EE - ExamSIDE.com

1

GATE EE 2023

MCQ (Single Correct Answer)

+1

-0.33

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

GATE EE 2023 Engineering Mathematics - Linear Algebra Question 14 English

A

$$\left[ {\matrix{ {{4 \over 5}} & {{3 \over 5}} \cr { - {3 \over 5}} & {{4 \over 5}} \cr } } \right]$$

B

$$\left[ {\matrix{ {{4 \over 5}} & { - {3 \over 5}} \cr {{3 \over 5}} & {{4 \over 5}} \cr } } \right]$$

C

$$\left[ {\matrix{ {{4 \over 5}} & {{3 \over 5}} \cr {{3 \over 5}} & {{4 \over 5}} \cr } } \right]$$

D

$$\left[ {\matrix{ {{4 \over 5}} & { - {3 \over 5}} \cr {{3 \over 5}} & { - {4 \over 5}} \cr } } \right]$$

2

GATE EE 2022

MCQ (Single Correct Answer)

+1

-0.33

Consider a 3 $$\times$$ 3 matrix A whose (i, j)-th element, a_i,j = (i $$-$$ j)³. Then the matrix A will be

A

symmetric

B

skew-symmetric

C

unitary

D

null

3

GATE EE 2021

MCQ (Single Correct Answer)

+1

-0.33

Let $p$ and $q$ be real numbers such that $p^2+q^2=1$. The eigen values of the matrix $\left[\begin{array}{cc}p & q \\ q & -p\end{array}\right]$ are

A

1 and 1

B

1 and -1

C

$j$ and $-j$

D

$p q$ and $-p q$

4

GATE EE 2017 Set 1

MCQ (Single Correct Answer)

+1

-0.3

The matrix $$A = \left[ {\matrix{ {{3 \over 2}} & 0 & {{1 \over 2}} \cr 0 & { - 1} & 0 \cr {{1 \over 2}} & 0 & {{3 \over 2}} \cr } } \right]$$ has three distinct eigen values and one of its eigen vectors is $$\left[ {\matrix{ 1 \cr 0 \cr 1 \cr } } \right].$$ Which one of the following can be another eigen vector of $$A$$?

A

$$\left[ {\matrix{ 0 \cr 0 \cr { - 1} \cr } } \right]$$

B

$$\left[ {\matrix{ { - 1} \cr 0 \cr 0 \cr } } \right]$$

C

$$\left[ {\matrix{ 1 \cr 0 \cr { - 1} \cr } } \right]$$

D

$$\left[ {\matrix{ 1 \cr { - 1} \cr 1 \cr } } \right]$$

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