1
GATE ECE 2006
+2
-0.6
The eigen values and the correspondinng eigen vectors of a $$2 \times 2$$ matrix are given by

Eigen value
$${\lambda _1} = 8$$
$${\lambda _2} = 4$$

Eigen vector
$${V_1} = \left[ {\matrix{ 1 \cr 1 \cr } } \right]$$
$${V_2} = \left[ {\matrix{ 1 \cr -1 \cr } } \right]$$

The matrix is

A
$$\left[ {\matrix{ 6 & 2 \cr 2 & 6 \cr } } \right]$$
B
$$\left[ {\matrix{ 4 & 6 \cr 6 & 4 \cr } } \right]$$
C
$$\left[ {\matrix{ 2 & 4 \cr 4 & 2 \cr } } \right]$$
D
$$\left[ {\matrix{ 4 & 8 \cr 8 & 4 \cr } } \right]$$
2
GATE ECE 2005
+2
-0.6
Given an orthogonal matrix $$A = \left[ {\matrix{ 1 & 1 & 1 & 1 \cr 1 & 1 & { - 1} & { - 1} \cr 1 & { - 1} & 0 & 0 \cr 0 & 0 & 1 & { - 1} \cr } } \right]$$ then the value of $${\left( {A{A^T}} \right)^{ - 1}}$$ is
A
$${1 \over 4}{{\rm I}_4}$$
B
$${1 \over 2}{{\rm I}_4}$$
C
$${\rm I}$$
D
$${1 \over 3}{{\rm I}_4}$$
3
GATE ECE 2005
+2
-0.6
Given the matrix $$\left[ {\matrix{ { - 4} & 2 \cr 4 & 3 \cr } } \right],$$ the eigen vector is
A
$$\left[ {\matrix{ 3 \cr 2 \cr } } \right]$$
B
$$\left[ {\matrix{ 4 \cr 3 \cr } } \right]$$
C
$$\left[ {\matrix{ 2 \cr { - 1} \cr } } \right]$$
D
$$\left[ {\matrix{ { - 2} \cr 1 \cr } } \right]$$
4
GATE ECE 2005
+2
-0.6
If $$A = \left[ {\matrix{ 2 & { - 0.1} \cr 0 & 3 \cr } } \right]$$ and $${A^{ - 1}} = \left[ {\matrix{ {{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}} & a \cr 0 & b \cr } } \right]$$ then $$a+b=$$
A
$${7 \over {20}}$$
B
$${3 \over {20}}$$
C
$${19 \over {60}}$$
D
$${11 \over {20}}$$
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