Moderate -0.8 This is a straightforward matrix multiplication with complex entries requiring careful arithmetic but no problem-solving or conceptual insight. The presence of complex numbers adds minor computational care, but the task is purely procedural—multiply rows by columns and simplify. Well below average difficulty for Further Maths.
11 The matrices \(\mathbf { A }\) and \(\mathbf { B }\) are given by
$$\mathbf { A } = \left[ \begin{array} { c c }
3 \mathrm { i } & - 2 \\
a & - \mathrm { i }
\end{array} \right] \quad \text { and } \quad \mathbf { B } = \left[ \begin{array} { c c }
4 & 5 \\
- 2 \mathrm { i } & - 1
\end{array} \right]$$
where \(a\) is a real number.
Calculate the product \(\mathbf { A B }\) in terms of \(a\)
Give your answer in its simplest form. [0pt]
[3 marks]
Correct method for at least two elements of AB: \(\mathbf{AB} = \begin{bmatrix} 3i & -2 \\ a & -i \end{bmatrix}\begin{bmatrix} 4 & 5 \\ -2i & -1 \end{bmatrix}\)
11 The matrices $\mathbf { A }$ and $\mathbf { B }$ are given by
$$\mathbf { A } = \left[ \begin{array} { c c }
3 \mathrm { i } & - 2 \\
a & - \mathrm { i }
\end{array} \right] \quad \text { and } \quad \mathbf { B } = \left[ \begin{array} { c c }
4 & 5 \\
- 2 \mathrm { i } & - 1
\end{array} \right]$$
where $a$ is a real number.
Calculate the product $\mathbf { A B }$ in terms of $a$\\
Give your answer in its simplest form.\\[0pt]
[3 marks]\\
\hfill \mbox{\textit{AQA Further AS Paper 1 2024 Q11 [3]}}