(a)

\begin{align*} \left( \begin{matrix} 3 & 4 \\ 8 & - 5 \end{matrix} \right) + \left( \begin{matrix} 4 & 6 \\ 3 & 0 \end{matrix} \right) & = \left( \begin{matrix} 7 & 10 \\ 11 & -5 \end{matrix} \right) \end{align*}

(b)

\begin{align*} \left( \begin{matrix} 7 \\ -8 \end{matrix} \right) + \left( \begin{matrix} 5 \\ -9 \end{matrix} \right) & = \left( \begin{matrix} 12 \\ -17 \end{matrix} \right) \end{align*}

(c)

\begin{align*} \left( \begin{matrix} 2 & 8 & -3 \end{matrix} \right) + \left( \begin{matrix} -4 & 7 & 0 \end{matrix} \right) & = \left( \begin{matrix} -2 & 15 & -3 \end{matrix} \right) \end{align*}

(d)

$$ \text{Not possible, since the matrices have different order} $$

(e)

\begin{align*} \left( \begin{matrix} 2 & -3 & 8 \\ 10 & 5 & 4 \end{matrix} \right) - \left( \begin{matrix} 5 & 6 & 7 \\ -3 & 0 & 12 \end{matrix} \right) & = \left( \begin{matrix} -3 & -9 & 1 \\ 13 & 5 & -8 \end{matrix} \right) \end{align*}

(f)

\begin{align*} \left( \begin{matrix} 12 \\ - 8.3 \\ 4 \end{matrix} \right) - \left( \begin{matrix} 8 \\ 1.7 \\ 0 \end{matrix} \right) & = \left( \begin{matrix} 4 \\ -10 \\ 4 \end{matrix} \right) \end{align*}

(g)

$$ \text{Not possible, since the matrices have different order} $$

(h)

\begin{align*} \left( \begin{matrix} 8 & 9 \\ -7 & 6 \end{matrix} \right) + \left( \begin{matrix} 4 & 0 \\ 8 & 0 \end{matrix} \right) & = \left( \begin{matrix} 12 & 9 \\ 1 & 6 \end{matrix} \right) \end{align*}

(a)

\begin{align*} \left( \begin{matrix} 3 \\ 4 \end{matrix} \right) + \left( \begin{matrix} -1 \\ 5 \end{matrix} \right) - \left( \begin{matrix} 6 \\ 7 \end{matrix} \right) & = \left( \begin{matrix} 2 \\ 9 \end{matrix} \right) - \left( \begin{matrix} 6 \\ 7 \end{matrix} \right) \\ & = \left( \begin{matrix} -4 \\ 2 \end{matrix} \right) \end{align*}

(b)

\begin{align*} \left( \begin{matrix} 4 & -1 \\ 3 & 2 \end{matrix} \right) + \left( \begin{matrix} 3 & 2 \\ -5 & 4 \end{matrix} \right) - \left( \begin{matrix} -6 & 4 \\ 2 & 1 \end{matrix} \right) & = \left( \begin{matrix} 7 & 1 \\ -2 & 6 \end{matrix} \right) - \left( \begin{matrix} -6 & 4 \\ 2 & 1 \end{matrix} \right) \\ & = \left( \begin{matrix} 13 & -3 \\ -4 & 5 \end{matrix} \right) \end{align*}

(c)

\begin{align*} \left( \begin{matrix} 1 & 3 \end{matrix} \right) - \left( \begin{matrix} 3 & 4 \end{matrix} \right) + \left( \begin{matrix} -2 & 6 \end{matrix} \right) & = \left( \begin{matrix} -2 & - 1 \end{matrix} \right) + \left( \begin{matrix} -2 & 6 \end{matrix} \right) \\ & = \left( \begin{matrix} -4 & 5 \end{matrix} \right) \end{align*}

(d)

\begin{align*} \left( \begin{matrix} 3 & 1 & 5 \\ -7 & 8 & - 2 \end{matrix} \right) - \left( \begin{matrix} 2 & -1 & 0 \\ 5 & - 2 & 6 \end{matrix} \right) + \left( \begin{matrix} 7 & 5 & 8 \\ -2 & 4 & -9 \end{matrix} \right) & = \left( \begin{matrix} 1 & 2 & 5 \\ -12 & 10 & -8 \end{matrix} \right) + \left( \begin{matrix} 7 & 5 & 8 \\ -2 & 4 & -9 \end{matrix} \right) \\ & = \left( \begin{matrix} 8 & 7 & 13 \\ -14 & 14 & -17 \end{matrix} \right) \end{align*}

(e)

$$ \text{Not possible, since the matrices have different order} $$

(f)

\begin{align*} \left( \begin{matrix} 4 & -3 \\ 2 & 5 \\ -8 & 9 \end{matrix} \right) - \left( \begin{matrix} -3 & 2 \\ 7 & - 1 \\ 6 & - 3 \end{matrix} \right) + \left( \begin{matrix} 4 & 5 \\ 0 & - 6 \\ 2 & 8 \end{matrix} \right) & = \left( \begin{matrix} 7 & -5 \\ -5 & 6 \\ -14 & 12 \end{matrix} \right) + \left( \begin{matrix} 4 & 5 \\ 0 & - 6 \\ 2 & 8 \end{matrix} \right) \\ & = \left( \begin{matrix} 11 & 0 \\ -5 & 0 \\ -12 & 20 \end{matrix} \right) \end{align*}

(g)

$$ \text{Not possible, since the matrices have different order} $$

(h)

\begin{align*} \left( \begin{matrix} 5 \end{matrix} \right) - \left( \begin{matrix} -6 \end{matrix} \right) + \left( \begin{matrix} 3 \end{matrix} \right) & = \left( \begin{matrix} 11 \end{matrix} \right) + \left( \begin{matrix} 3 \end{matrix} \right) \\ & = \left( \begin{matrix} 14 \end{matrix} \right) \end{align*}

(i)

\begin{align*} \textbf{Q} & = \left( \begin{matrix} 42 & 35 & 38 \\ 33 & 40 & 37 \end{matrix} \right) \end{align*}

(ii)

\begin{align*} \textbf{P} + \textbf{Q} & = \left( \begin{matrix} 41 & 38 & 29 \\ 39 & 33 & 36 \end{matrix} \right) + \left( \begin{matrix} 42 & 35 & 38 \\ 33 & 40 & 37 \end{matrix} \right) \\ & = \left( \begin{matrix} 83 & 73 & 67 \\ 72 & 73 & 73 \end{matrix} \right) \end{align*}

(iii)

\begin{align} & \text{It represents the total marks each student obtained for the Mathematics test} \\ & \text{and for the English test respectively.} \end{align}

(i)

\begin{align*} \textbf{A} + \textbf{B} & = \left( \begin{matrix} 5 & -5 \\ -4 & 9 \end{matrix} \right) + \left( \begin{matrix} 1 & 3 \\ -2 & 4 \end{matrix} \right) \\ & = \left( \begin{matrix} 6 & -2 \\ -6 & 13 \end{matrix} \right) \end{align*}

(ii)

\begin{align*} \textbf{B} + \textbf{A} & = \left( \begin{matrix} 1 & 3 \\ -2 & 4 \end{matrix} \right) + \left( \begin{matrix} 5 & -5 \\ -4 & 9 \end{matrix} \right) \\ & = \left( \begin{matrix} 6 & -2 \\ -6 & 13 \end{matrix} \right) \end{align*}

(iii)

\begin{align*} \textbf{B} + \textbf{C} & = \left( \begin{matrix} 1 & 3 \\ -2 & 4 \end{matrix} \right) + \left( \begin{matrix} 0 & 2 \\ -1 & 4 \end{matrix} \right) \\ & = \left( \begin{matrix} 1 & 5 \\ -3 & 8 \end{matrix} \right) \end{align*}

(iv)

\begin{align*} \textbf{C} + \textbf{B} & = \left( \begin{matrix} 0 & 2 \\ -1 & 4 \end{matrix} \right) + \left( \begin{matrix} 1 & 3 \\ -2 & 4 \end{matrix} \right) \\ & = \left( \begin{matrix} 1 & 5 \\ -3 & 8 \end{matrix} \right) \end{align*}

(v) For B + C, use the result from iii.

\begin{align*} \textbf{A} + (\textbf{B} + \textbf{C}) & = \left( \begin{matrix} 5 & -5 \\ -4 & 9 \end{matrix} \right) + \left( \begin{matrix} 1 & 5 \\ -3 & 8 \end{matrix} \right) \\ & = \left( \begin{matrix} 6 & 0 \\ -7 & 17 \end{matrix} \right) \end{align*}

(vi) For A + B, use the result from i.

\begin{align*} (\textbf{A} + \textbf{B}) + \textbf{C} & = \left( \begin{matrix} 6 & -2 \\ -6 & 13 \end{matrix} \right) + \left( \begin{matrix} 0 & 2 \\ -1 & 4 \end{matrix} \right) \\ & = \left( \begin{matrix} 6 & 0 \\ -7 & 17 \end{matrix} \right) \end{align*}

(i)

\begin{align*} \textbf{A} - \textbf{B} & = \left( \begin{matrix} 3 & 1 \\ 4 & - 2 \end{matrix} \right) - \left( \begin{matrix} 4 & -1 \\ 3 & -4 \end{matrix} \right) \\ & = \left( \begin{matrix} -1 & 2 \\ 1 & 2 \end{matrix} \right) \end{align*}

(ii)

\begin{align*} \textbf{B} - \textbf{A} & = \left( \begin{matrix} 4 & -1 \\ 3 & -4 \end{matrix} \right) - \left( \begin{matrix} 3 & 1 \\ 4 & - 2 \end{matrix} \right) \\ & = \left( \begin{matrix} 1 & -2 \\ -1 & -2 \end{matrix} \right) \end{align*}

(iii)

\begin{align*} \textbf{B} - \textbf{C} & = \left( \begin{matrix} 4 & -1 \\ 3 & -4 \end{matrix} \right) - \left( \begin{matrix} 0 & 1 \\ -1 & 0 \end{matrix} \right) \\ & = \left( \begin{matrix} 4 & -2 \\ 4 & -4 \end{matrix} \right) \end{align*}

(iv) For B - C, use the result from iii.

\begin{align*} \textbf{A} - (\textbf{B} - \textbf{C}) & = \left( \begin{matrix} 3 & 1 \\ 4 & -2 \end{matrix} \right) - \left( \begin{matrix} 4 & -2 \\ 4 & -4 \end{matrix} \right) \\ & = \left( \begin{matrix} -1 & 3 \\ 0 & 2 \end{matrix} \right) \end{align*}

(v) For A - B, use the result from i.

\begin{align*} (\textbf{A} - \textbf{B}) - \textbf{C} & = \left( \begin{matrix} -1 & 2 \\ 1 & 2 \end{matrix} \right) - \left( \begin{matrix} 0 & 1 \\ -1 & 0 \end{matrix} \right) \\ & = \left( \begin{matrix} -1 & 1 \\ 2 & 2 \end{matrix} \right) \end{align*}

(i)

\begin{align*} \textbf{A} - \textbf{B}) & = \left( \begin{matrix} 240 & 210 & 195 & 304 & 195 \\ 95 & 120 & 116 & 102 & 100 \\ 100 & 94 & 132 & 132 & 110 \end{matrix} \right) - \left( \begin{matrix} 24 & 13 & 5 & 11 & 27 \\ 12 & 18 & 9 & 17 & 13 \\ 10 & 14 & 12 & 21 & 8 \end{matrix} \right) \\ & = \left( \begin{matrix} 216 & 197 & 190 & 293 & 168 \\ 83 & 102 & 107 & 85 & 87 \\ 90 & 80 & 120 & 111 & 102 \end{matrix} \right) \end{align*}

(ii)

\begin{align} & \text{The number of Chinese, Malay and Tamil textbooks for Secondary 1, 2, 3, 4 and 5} \\ & \text{sold in the school bookshop.} \end{align}