1. **Stating the problem:** We are asked to perform matrix multiplications and solve for unknown variables in given matrix equations. 2. **Matrix multiplication formula:** For matrices $A$ of size $m \times n$ and $B$ of size $n \times p$, the product $AB$ is an $m \times p$ matrix where each element is computed as: $$ (AB)_{ij} = \sum_{k=1}^n A_{ik} B_{kj} $$ 3. **Example a.ii:** Multiply $$ \begin{pmatrix}1 & 2 \\ 8 & -2\end{pmatrix} \times \begin{pmatrix}-2 & 2 \\ \text{(2x2)}\end{pmatrix} $$ Since the second matrix is incomplete, we skip this. 4. **Example b:** Given $$ \begin{pmatrix}4 & 2f\end{pmatrix} \times \begin{pmatrix}-\frac{7}{3}\end{pmatrix} = \begin{pmatrix}-34\end{pmatrix} $$ This is a multiplication of a $1 \times 2$ matrix by a $2 \times 1$ matrix (assuming the second matrix is $\begin{pmatrix}-\frac{7}{3} \\ ?\end{pmatrix}$ but incomplete). Since incomplete, skip. 5. **Example c:** Given $$ \begin{pmatrix}1 & 7\end{pmatrix} \times \begin{pmatrix}x & 1 \\ -2 & 2\end{pmatrix} = \begin{pmatrix}-11 & 15\end{pmatrix} $$ We want to find $x$. 6. **Step-by-step for c:** Multiply the $1 \times 2$ matrix by the $2 \times 2$ matrix: $$ \begin{pmatrix}1 & 7\end{pmatrix} \times \begin{pmatrix}x & 1 \\ -2 & 2\end{pmatrix} = \begin{pmatrix}1 \cdot x + 7 \cdot (-2) & 1 \cdot 1 + 7 \cdot 2\end{pmatrix} = \begin{pmatrix}x - 14 & 1 + 14\end{pmatrix} = \begin{pmatrix}x - 14 & 15\end{pmatrix} $$ 7. **Set equal to given result:** $$ \begin{pmatrix}x - 14 & 15\end{pmatrix} = \begin{pmatrix}-11 & 15\end{pmatrix} $$ 8. **Equate components:** $$ x - 14 = -11 $$ 9. **Solve for $x$:** $$ x = -11 + 14 = 3 $$ **Final answer:** $x = 3$