JAMB Mathematics 2013 Paper

Concept:Matrix scalar multiplication and addition are performed element-wise.First multiply each entry of matrix $P$ by the scalar $2$, then add the corresponding entries of matrix $Q$.Explanation:Given $P = \begin{pmatrix} 5 & 3 \\ 2 & 1 \end{pmatrix}$ and $Q = \begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}$.Compute $2P$ by multiplying every element of $P$ by $2$.$$2P = \begin{pmatrix} 2(5) & 2(3) \\ 2(2) & 2(1) \end{pmatrix} = \begin{pmatrix} 10 & 6 \\ 4 & 2 \end{pmatrix}$$Now add $2P$ and $Q$ by adding the entries in the same positions.$$2P + Q = \begin{pmatrix} 10 & 6 \\ 4 & 2 \end{pmatrix} + \begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}$$$$= \begin{pmatrix} 10+4 & 6+2 \\ 4+3 & 2+5 \end{pmatrix} = \begin{pmatrix} 14 & 8 \\ 7 & 7 \end{pmatrix}$$The resulting $2 \times 2$ matrix has first row $14, 8$ and second row $7, 7$.Answer:$$2P + Q = \begin{pmatrix} 14 & 8 \\ 7 & 7 \end{pmatrix}$$This corresponds to the matrix in option B.