Edexcel F1 2017 June — Question 2 4 marks

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2017
SessionJune
Marks4
PaperDownload PDF ↗
Topic3x3 Matrices
TypeMatrix equation solving (AB = C)
DifficultyModerate -0.5 This is a straightforward Further Maths question requiring matrix multiplication (routine calculation) followed by finding a determinant of a 2×2 matrix and solving a simple equation. While it involves 3×3 matrices, the operations are mechanical with no conceptual challenges or novel problem-solving required.
Spec4.03b Matrix operations: addition, multiplication, scalar4.03j Determinant 3x3: calculation

2. Given that $$\mathbf { A } = \left( \begin{array} { r r r } 3 & 1 & - 2 \\ - 1 & 0 & 5 \end{array} \right) \text { and } \mathbf { B } = \left( \begin{array} { r r } 2 & 4 \\ - k & 2 k \\ 3 & 0 \end{array} \right) , \text { where } k \text { is a constant }$$
  1. find the matrix \(\mathbf { A B }\),
  2. find the exact value of \(k\) for which \(\operatorname { det } ( \mathbf { A B } ) = 0\)

2. Given that

$$\mathbf { A } = \left( \begin{array} { r r r } 
3 & 1 & - 2 \\
- 1 & 0 & 5
\end{array} \right) \text { and } \mathbf { B } = \left( \begin{array} { r r } 
2 & 4 \\
- k & 2 k \\
3 & 0
\end{array} \right) , \text { where } k \text { is a constant }$$
\begin{enumerate}[label=(\alph*)]
\item find the matrix $\mathbf { A B }$,
\item find the exact value of $k$ for which $\operatorname { det } ( \mathbf { A B } ) = 0$
\end{enumerate}

\hfill \mbox{\textit{Edexcel F1 2017 Q2 [4]}}