The additive inverse of matrix A + B, where

A = $\begin{bmatrix$}[r] 4 & 2 \ 7 & -2 \end{bmatrix} \text{ and } B = \begin{bmatrix}[r] -2 & 1 \ 3 & -4 \end{bmatrix} is :

1. $\begin{bmatrix$}[r] -2 & -3 \ -10 & 6 \end{bmatrix}

2. $\begin{bmatrix$}[r] 2 & 3 \ -10 & -6 \end{bmatrix}

3. $\begin{bmatrix$}[r] -2 & -3 \ -10 & -6 \end{bmatrix}

4. $\begin{bmatrix$}[r] -2 & 3 \ 10 & -6 \end{bmatrix}

State, whether the following statements are true or false. If false, give a reason.

(i) If A and B are two matrices of orders 3 × 2 and 2 × 3 respectively; then their sum A + B is possible.

(ii) The matrices A_{2 × 3} and B_{2 × 3} are conformable for subtraction.

(iii) Transpose of a 2 × 1 matrix is a 2 × 1 matrix.

(iv) Transpose of a square matrix is a square matrix.

(v) A column matrix has many columns and only one row.

Solve for a, b and c; if :

$\begin{bmatrix} a & a - b \ b + c & 0 \end{bmatrix} = \begin{bmatrix} 3 & -1 \ 2 & 0 \end{bmatrix}$

Wherever possible, write each of the following as a single matrix.

(i) $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} + \begin{bmatrix} -1 & -2 \ 1 & -7 \end{bmatrix}$

(ii) $\begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \end{bmatrix} - \begin{bmatrix} 0 & 2 & 3 \ 6 & -1 & 0 \end{bmatrix}$

(iii) $\begin{bmatrix} 0 & 1 & 2 \ 4 & 6 & 7 \end{bmatrix} + \begin{bmatrix} 3 & 4 \ 6 & 8 \end{bmatrix}$