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

Given the matrix $$\left[ {\matrix{ { - 4} & 2 \cr 4 & 3 \cr } } \right],$$ the eigen vector is

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

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 $$a+b=$$