The rank of the matrix $$\left[ {\matrix{ 1 & 1 & 1 \cr 1 & { - 1} & 0 \cr 1 & 1 & 1 \cr } } \right]$$ is

The eigen values of the matrix $$\left[ {\matrix{ 2 & { - 1} & 0 & 0 \cr 0 & 3 & 0 & 0 \cr 0 & 0 & { - 2} & 0 \cr 0 & 0 & { - 1} & 4 \cr } } \right]$$ are

The eigen values of the matrix $$A = \left[ {\matrix{ 0 & 1 \cr 1 & 0 \cr } } \right]$$ are

The following system of equations
$${{x_1} + {x_2} + {x_3} = 3}$$
$${{x_1} - {x_3} = 0}$$
$${{x_1} - {x_2} + {x_3} = 1}$$ has