1
GATE EE 2025
MCQ (Single Correct Answer)
+1
-0.33

Let $P=\left[\begin{array}{ccc}2 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{array}\right]$ and let $I$ be the identity matrix. Then $P^2$ is equal to

A
$2 P-I$
B
$P$
C
$I$
D
$P+I$
2
GATE EE 2024
MCQ (Single Correct Answer)
+1
-0.33

Which one of the following matrices has an inverse?

A

$$\begin{bmatrix} 1 & 4 & 8 \\ 0 & 4 & 2 \\ 0.5 & 2 & 4 \end{bmatrix}$$

B

$$\begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 2 & 9 \end{bmatrix}$$

C

$$\begin{bmatrix} 1 & 4 & 8 \\ 0 & 4 & 2 \\ 1 & 2 & 4 \end{bmatrix}$$

D

$$\begin{bmatrix} 1 & 4 & 8 \\ 0 & 4 & 2 \\ 3 & 12 & 24 \end{bmatrix}$$

3
GATE EE 2024
Numerical
+1
-0

The sum of the eigenvalues of the matrix $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}^2$ is ______ (rounded off to the nearest integer).

Your input ____
4
GATE EE 2023
MCQ (Single Correct Answer)
+1
-0.33

For a given vector $${[\matrix{ 1 & 2 & 3 \cr } ]^T}$$, the vector normal to the plane defined by $${w^T}x = 1$$ is

A
$${[\matrix{ { - 2} & { - 2} & 2 \cr } ]^T}$$
B
$${[\matrix{ 3 & 0 & { - 1} \cr } ]^T}$$
C
$${[\matrix{ 3 & 2 & 1 \cr } ]^T}$$
D
$${[\matrix{ 1 & 2 & 3 \cr } ]^T}$$
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