1
GATE ME 2024
+2
-1.33

The matrix $\begin{bmatrix} 1 & a \\ 8 & 3 \end{bmatrix}$ (where $a > 0$) has a negative eigenvalue if $a$ is greater than

A

$\frac{3}{8}$

B

$\frac{1}{8}$

C

$\frac{1}{4}$

D

$\frac{1}{5}$

2
GATE ME 2017 Set 2
Numerical
+2
-0
Consider the matrix $$A = \left[ {\matrix{ {50} & {70} \cr {70} & {80} \cr } } \right]$$ whose eigenvectors corresponding to eigen values $${\lambda _1}$$ and $${\lambda _2}$$ are $${x_1} = \left[ {\matrix{ {70} \cr {{\lambda _1} - 50} \cr } } \right]$$ and $${x_2} = \left[ {\matrix{ {{\lambda _2} - 80} \cr {70} \cr } } \right],$$ respectively. The value of $$x_1^T{x_2}$$ is ________
3
GATE ME 2016 Set 3
Numerical
+2
-0
The number of linear independent eigenvectors of matrix $$A = \left[ {\matrix{ 2 & 1 & 0 \cr 0 & 2 & 0 \cr 0 & 0 & 3 \cr } } \right]$$ is ________.
4
GATE ME 2015 Set 3
+2
-0.6
For a given matrix $$P = \left[ {\matrix{ {4 + 3i} & { - i} \cr i & {4 - 3i} \cr } } \right],$$ where $$i = \sqrt { - 1} ,$$ the inverse of matrix $$P$$ is
A
$${1 \over {24}}\left[ {\matrix{ {4 - 3i} & i \cr { - i} & {4 + 3i} \cr } } \right]$$
B
$${1 \over {25}}\left[ {\matrix{ i & {4 - 3i} \cr {4 + 3i} & i \cr } } \right]$$
C
$${1 \over {24}}\left[ {\matrix{ {4 + 3i} & { - i} \cr i & {4 - 3i} \cr } } \right]$$
D
$${1 \over {25}}\left[ {\matrix{ {4 + 3i} & { - i} \cr i & {4 - 3i} \cr } } \right]$$
GATE ME Subjects
EXAM MAP
Medical
NEET