WAEC 2018 · Paper 2 · Q3

(a)
Given that $B = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix}$ and $B^2 + 3B + 2I = 3N$ , where $I$ is the $2 \times 2$ unit matrix, find the matrix $N$ .
Show the answer
$N = \begin{pmatrix} 5 & 9 \\ 3 & 11 \end{pmatrix}$

Worked solution (try it first)

$B^2 = \begin{pmatrix} 4 + 3 & 6 + 12 \\ 2 + 4 & 3 + 16 \end{pmatrix}$
$= \begin{pmatrix} 7 & 18 \\ 6 & 19 \end{pmatrix}$ .
$3B = \begin{pmatrix} 6 & 9 \\ 3 & 12 \end{pmatrix}$ and $2I = \begin{pmatrix} 2 & 0 \\ 0 & 2 \end{pmatrix}$ .
$3N = B^2 + 3B + 2I$
$= \begin{pmatrix} 15 & 27 \\ 9 & 33 \end{pmatrix}$ .
So $N = \begin{pmatrix} 5 & 9 \\ 3 & 11 \end{pmatrix}$ .