Moderate -0.8 This is a straightforward matrix arithmetic question requiring students to subtract matrices, equate corresponding elements, and solve a simple system of linear equations. It involves only basic matrix operations and algebraic manipulation with no conceptual depth or problem-solving insight required—significantly easier than average A-level questions.
1.
$$\left( \begin{array} { l l }
x & 9 \\
y & z
\end{array} \right) - 3 \left( \begin{array} { l l }
z & y \\
z & y
\end{array} \right) = k \mathbf { I }$$
where \(x , y , z\) and \(k\) are constants.
Determine the value of \(x\), the value of \(y\) and the value of \(z\).
AO 1.1b — Follow through on the value of \(z\) which comes from their \(y\) divided by 3
Uses \(z - 3y = k \Rightarrow k = -8\) and \(x - 3z = k \Rightarrow x = k + 3z = \text{their } k + 3 \times \text{their } z\), leading to a value for \(x\). Alternatively uses \(x - 3z = k = z - 3y\) with values for \(y\) and \(z\) to find a value for \(x\).
M1
AO 3.1a — Complete method to find \(x\). Condone a slip with coefficients if intention is clear but must have correct letters.
\(x = -5\)
A1
AO 1.1b — Correct answer only scores full marks.
(4)
(4 marks)
## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $y = 3$ | B1 | AO 2.2a |
| $z = \dfrac{\text{their } y}{3} = \ldots \{1\}$ | B1ft | AO 1.1b — Follow through on the value of $z$ which comes from their $y$ divided by 3 |
| Uses $z - 3y = k \Rightarrow k = -8$ and $x - 3z = k \Rightarrow x = k + 3z = \text{their } k + 3 \times \text{their } z$, leading to a value for $x$. **Alternatively** uses $x - 3z = k = z - 3y$ with values for $y$ and $z$ to find a value for $x$. | M1 | AO 3.1a — Complete method to find $x$. Condone a slip with coefficients if intention is clear but must have correct letters. |
| $x = -5$ | A1 | AO 1.1b — Correct answer only scores full marks. |
| **(4)** | | **(4 marks)** |
1.
$$\left( \begin{array} { l l }
x & 9 \\
y & z
\end{array} \right) - 3 \left( \begin{array} { l l }
z & y \\
z & y
\end{array} \right) = k \mathbf { I }$$
where $x , y , z$ and $k$ are constants.\\
Determine the value of $x$, the value of $y$ and the value of $z$.
\hfill \mbox{\textit{Edexcel CP AS 2023 Q1 [4]}}