1
GATE ECE 2009
+2
-0.6
The eigen values of the following matrix $$\left[ {\matrix{ { - 1} & 3 & 5 \cr { - 3} & { - 1} & 6 \cr 0 & 0 & 3 \cr } } \right]$$ are
A
$$3, 3 + 5j, 6 - j$$
B
$$-6 + 5j, 3 + j, 3 - j$$
C
$$3+j, 3-j, 5+j$$
D
$$3, -1+3j, -1-3j$$
2
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
$$\left[ {\matrix{ 4 & 8 \cr 8 & 4 \cr } } \right]$$
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
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
$${1 \over 3}{{\rm I}_4}$$
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