How many of the following matrices have an eigen value $$1$$?
$$\left[ {\matrix{ 1 & 0 \cr 0 & 0 \cr } } \right],\,\,\left[ {\matrix{ 0 & 1 \cr 0 & 0 \cr } } \right],\,\,\left[ {\matrix{ 1 & { - 1} \cr 1 & 1 \cr } } \right]\,\,and\,\,\left[ {\matrix{ { - 1} & 0 \cr 1 & { - 1} \cr } } \right]$$

What is the size of the smallest MIS (Maximal Independent Set) of a chain of nine nodes?

The following system of equations
$${x_1}\, + \,{x_2}\, + 2{x_3}\, = 1$$
$${x_1}\, + \,2 {x_2}\, + 3{x_3}\, = 2$$
$${x_1}\, + \,4{x_2}\, + a{x_3}\, = 4$$ has a unique solution. The only possible value (s) for $$\alpha $$ is/are

If $$P, Q, R$$ are subsets of the universal set $$U$$, then
$$\left( {P \cap Q \cap R} \right) \cup \left( {{P^c} \cap Q \cap R} \right) \cup {Q^c} \cup {R^c}$$ is