Problem

4. (i) $A = \begin{pmatrix} 3 & -1 \\ -3 & k \end{pmatrix}$ where $k$ is a constant

The transformation represented by $A$ transforms triangle $T$ to triangle $T'$

The area of triangle $T'$ is three times the area of triangle $T$

Determine the possible values of $k$

(ii) $B = \begin{pmatrix} a-4 & -2 \\ 2 & 3 \end{pmatrix}$ and $BC = \begin{pmatrix} 5 & 1 \\ 1 & 4 \end{pmatrix}$ where $a$ is a constant

Determine, in terms of $a$, the matrix $C$