Classify the following matrices :

$\text{(i) }\begin{bmatrix$}[r] 2 & -1 \ 5 & 1 \end{bmatrix} \\[0.5em]

$\text{(ii) } \begin{bmatrix} 2 & 3 & -7 \end{bmatrix} \\[0.5em]$

$\text{(iii) } \begin{bmatrix$}[r] 3 \ 0 \ -1 \end{bmatrix} \\[0.5em]

$\text{(iv) } \begin{bmatrix} 2 & -4 \ 0 & 0 \ 1 & 7 \end{bmatrix} \\[0.5em]$

$\text{(v) } \begin{bmatrix$}[r] 2 & 7 & 8 \ -1 & \sqrt{2} & 0 \end{bmatrix} \\[0.5em]

$\text{(vi) } \begin{bmatrix} 0 & 0 & 0 \ 0 & 0 & 0 \end{bmatrix}. \\[0.5em]$

If a matrix has 8 elements, what are the possible orders it can have ?

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}.