What are the eigen values of the following $$2x2$$ matrix? $$$\left[ {\matrix{ 2 & { - 1} \cr { - 4} & 5 \cr } } \right]$$$

Consider the following system of equations in three real variables $$x1, x2$$ and $$x3$$ :
$$2x1 - x2 + 3x3 = 1$$
$$3x1 + 2x2 + 5x3 = 2$$
$$ - x1 + 4x2 + x3 = 3$$
This system of equations has

In an M$$ \times $$N matrix such that all non-zero entries are covered in $$a$$ rows and $$b$$ columns. Then the maximum number of non-zero entries, such that no two are on the same row or column, is

If matrix $$X = \left[ {\matrix{ a & 1 \cr { - {a^2} + a - 1} & {1 - a} \cr } } \right]$$
and $${X^2} - X + 1 = 0$$
($${\rm I}$$ is the identity matrix and $$O$$ is the zero matrix), then the inverse of $$X$$ is