1
GATE CE 2023 Set 2
MCQ (More than One Correct Answer)
+1
-0

For the matrix

$\rm [A]=\begin{bmatrix}1&-1&0\\\ -1&2&-1\\\ 0&-1&1\end{bmatrix}$

which of the following statements is/are TRUE?

A
[𝐴]{𝑥} = {𝑏} has a unique solution
B
[𝐴]{𝑥} = {𝑏} does not have a unique solution 
C
[𝐴] has three linearly independent eigenvectors
D
[𝐴] is a positive definite matrix
2
GATE CE 2023 Set 1
MCQ (More than One Correct Answer)
+1
-0
If M is an arbitrary real n × n matrix, then which of the following matrices will have non-negative eigenvalues? 
A
M2
B
MMT
C
MTM
D
(MT)2
3
GATE CE 2022 Set 2
MCQ (More than One Correct Answer)
+1
-0

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

A
yyT is symmetric matrix
B
yyT is invertible
C
yyT has a rank of 2022
D
yTy is an eigen value of yyT.
4
GATE CE 2022 Set 2
Numerical
+1
-0

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)

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