GATE CE 2023 Set 1 | Linear Algebra Question 11 | Engineering Mathematics

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GATE CE 2023 Set 1

MCQ (More than One Correct Answer)

-0

If M is an arbitrary real n × n matrix, then which of the following matrices will have non-negative eigenvalues?

MMT

MTM

(MT)2

GATE CE 2022 Set 2

MCQ (More than One Correct Answer)

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Let y be a non-zero vector of size 2022 $$\times$$ 1. Which of the following statements is/are TRUE?

yy^T is symmetric matrix

yy^T is invertible

yy^T has a rank of 2022

y^Ty is an eigen value of yy^T.

GATE CE 2022 Set 2

Numerical

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The components of pure shear strain in a sheared are given in the matrix form:

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

Here, Trace ($$\varepsilon $$) = 0. Given, P = Trace ($$\varepsilon$$⁸) and Q = Trace ($$\varepsilon $$¹¹).

The numerical value of (P + Q) is ___________. (in integer)

Your input ____

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 $${[PQ]^{ - 1}} = {Q^{ - 1}}{P^{ - 1}}$$.

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