GATE CE 2022 Set 2 | Linear Algebra Question 15 | Engineering Mathematics

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GATE CE 2022 Set 2

MCQ (More than One Correct Answer)

-0

P and Q are two square matrices of the same order. Which of the following statements is/are correct?

If P and Q are invertible, then$${[PQ]^{ - 1}} = {Q^{ - 1}}{P^{ - 1}}$$.

If P and Q are invertible, then $${[PQ]^{ - 1}} = {P^{ - 1}}{Q^{ - 1}}$$.

If P and Q are invertible, then $${[QP]^{ - 1}} = {P^{ - 1}}{Q^{ - 1}}$$.

If P and Q are not invertible, then $${[PQ]^{ - 1}} = {Q^{ - 1}}{P^{ - 1}}$$.

GATE CE 2022 Set 1

MCQ (More than One Correct Answer)

-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?

$$-$$20

$$-$$30

GATE CE 2022 Set 1

MCQ (Single Correct Answer)

-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

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

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

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

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

GATE CE 2017 Set 1

MCQ (Single Correct Answer)

-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?

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

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

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

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

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