| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Topic | 3x3 Matrices |
| Type | Matrix equation solving (AB = C) |
| Difficulty | Standard +0.3 This is a straightforward matrix equation problem requiring students to recognize that M must be a 1×2 matrix (from dimension analysis), set up equations by comparing entries after multiplication, and solve a simple system. While it involves 3D thinking about matrix dimensions and requires careful algebraic manipulation, it's a standard textbook exercise with a clear method and no novel insight required. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar4.03c Matrix multiplication: properties (associative, not commutative) |
1.
The matrix $\mathbf { M }$ is such that $\mathbf { M } \left( \begin{array} { r r r } 1 & 0 & k \\ 2 & - 1 & 1 \end{array} \right) = \left( \begin{array} { l l l } 1 & - 2 & 0 \end{array} \right)$.\\
Find
\begin{itemize}
\item the matrix $\mathbf { M }$,
\item the value of the constant $k$.\\[0pt]
\end{itemize}
\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q1 [6]}}