GATE CE 2022 Set 1 | Linear Algebra Question 16 | Engineering Mathematics | GATE CE - ExamSIDE.com

1

GATE CE 2022 Set 1

MCQ (More than One Correct Answer)

+1

-0

The matrix M is defined as

$$M = \left[ {\matrix{ 1 & 3 \cr 4 & 2 \cr } } \right]$$

and has eigenvalues 5 and $$-$$2. The matrix Q is formed as

Q = M³ $$-$$ 4M² $$-$$ 2M

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

A

15

B

25

C

$$-$$20

D

$$-$$30

2

GATE CE 2022 Set 1

MCQ (Single Correct Answer)

+1

-0.33

The Cartesian coordinates of a point P in a right-handed coordinate system are (1, 1, 1). The transformed coordinates of P due to a 45$$^\circ$$ clockwise rotation of the coordinate system about the positive x-axis are

A

(1, 0, $$\sqrt 2 $$)

B

(1, 0, $$-$$$$\sqrt 2 $$)

C

($$-$$1, 0, $$\sqrt 2 $$)

D

($$-$$1, 0, $$-$$$$\sqrt 2 $$)

3

GATE CE 2017 Set 2

MCQ (Single Correct Answer)

+1

-0.3

Consider the following simultaneous equations (with $${c_1}$$ and $${c_2}$$ being constants): $$$3{x_1} + 2{x_2} = {c_1}$$$ $$$4{x_1} + {x_2} = {c_2}$$$

The characteristic equation for these simultaneous equation is

A

$${\lambda ^2} - 4\lambda - 5 = 0$$

B

$${\lambda ^2} 4\lambda + 5 = 0$$

C

$${\lambda ^2} + 4\lambda - 5 = 0$$

D

$${\lambda ^2} + 4\lambda + 5 = 0$$

4

GATE CE 2017 Set 1

MCQ (Single Correct Answer)

+1

-0.3

The matrix $$P$$ is the inverse of a matrix $$Q.$$ If $${\rm I}$$ denotes the identity matrix, which one of the following options is correct?

A

$$PQ = {\rm I}\,\,\,but\,\,\,QP \ne {\rm I}$$

B

$$QP = {\rm I}\,\,\,but\,\,\,PQ \ne {\rm I}$$

C

$$PQ = {\rm I}\,\,\,and\,\,\,QP = {\rm I}$$

D

$$PQ - QP = {\rm I}$$

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