Construct a 2 $\times$ 2 matrix whose elements a_ij are given by

(i) a_ij = 2i - j

(ii) a_ij = i.j

Find the values of x and y if $\begin{bmatrix$}[r] 2x + y \ 3x - 2y \end{bmatrix} = \begin{bmatrix} 5 \ 4 \end{bmatrix}.

If $\begin{bmatrix$}[r] x + 3 & 4 \ y - 4 & x + y \end{bmatrix} = \begin{bmatrix}[r] 5 & 4 \ 3 & 9 \end{bmatrix}, find the values of x and y.

Find the values of x, y and z if $\begin{bmatrix$}[r] x + 2 & 6 \ 3 & 5z \end{bmatrix} = \begin{bmatrix}[r] -5 & y^2 + y \ 3 & -20 \end{bmatrix} .