Perform the following operations.
(a) \left [ \begin{matrix} 2 & 3 \\ 4 & 1 \end{matrix} \right ] + \left [ \begin{matrix} 5 & 1 \\ -2 & 7 \end{matrix} \right ]
(b) \left [ \begin{matrix} 3 & 0 \\ 1 & -5 \end{matrix} \right ] - \left [ \begin{matrix} 1 & -1 \\ -2 & 0 \end{matrix} \right ]
(c) 5 \left [ \begin{matrix} 2 & 3 \\ 4 & 1 \end{matrix} \right ]
(d) 2 \left [ \begin{matrix} 1 & 3 \\ 0 & -1 \end{matrix} \right ] + 3 \left [ \begin{matrix} 4 & 0 \\ 1 & 2 \end{matrix} \right ]
(a) \left [ \begin{matrix} 2 & 3 \\ 4 & 1 \end{matrix} \right ] + \left [ \begin{matrix} 5 & 1 \\ -2 & 7 \end{matrix} \right ] = \left [ \begin{matrix} 2 + 5 & 3 + 1 \\ 4 + (-2) & 1 + 7 \end{matrix} \right ] = \left [ \begin{matrix} 7 & 4 \\ 2 & 8 \end{matrix} \right ]
(b) \left [ \begin{matrix} 3 & 0 \\ 1 & -5 \end{matrix} \right ] – \left [ \begin{matrix} 1 & -1 \\ -2 & 0 \end{matrix} \right ] = \left [ \begin{matrix} 3 – 1 & 0 – (-1) \\ 1 – (-2) & -5 – 0 \end{matrix} \right ] = \left [ \begin{matrix} 7 & 4 \\ 2 & 8 \end{matrix} \right ]
(c) 5 \left [ \begin{matrix} 2 & 3 \\ 4 & 1 \end{matrix} \right ] = \left [ \begin{matrix} 5(2) & 5(3) \\ 5(4) & 5(1) \end{matrix} \right ] = \left [ \begin{matrix} 10 & 15 \\ 20 & 5 \end{matrix} \right ]
(d) 2 \left [ \begin{matrix} 1 & 3 \\ 0 & -1 \end{matrix} \right ] + 3 \left [ \begin{matrix} 4 & 0 \\ 1 & 2 \end{matrix} \right ] = \left [ \begin{matrix} 2 & 6 \\ 0 & -2 \end{matrix} \right ] + \left [ \begin{matrix} 12 & 0 \\ 3 & 6 \end{matrix} \right ] = \left [ \begin{matrix} 2 + 12 & 6 + 0 \\ 0 + 3 & -2 + 6 \end{matrix} \right ] = \left [ \begin{matrix} 14 & 6 \\ 3 & 4 \end{matrix} \right ]