OCR MEI Further Pure Core AS 2024 June — Question 2 5 marks

Exam BoardOCR MEI
ModuleFurther Pure Core AS (Further Pure Core AS)
Year2024
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMatrices
TypeProperties of matrix operations
DifficultyEasy -1.2 This is a straightforward verification question requiring routine matrix multiplication (computing BC, A(BC), AB, then (AB)C) followed by recalling the associative property. It's purely mechanical calculation with no problem-solving or insight required, making it easier than average but not trivial due to the computational work involved.
Spec4.03b Matrix operations: addition, multiplication, scalar4.03c Matrix multiplication: properties (associative, not commutative)
2 The matrices \(\mathbf { A } , \mathbf { B }\) and \(\mathbf { C }\) are given by \(\mathbf { A } = \left( \begin{array} { r r } 1 & a \\ - 1 & 2 \end{array} \right) , \mathbf { B } = \left( \begin{array} { r r } 2 & 0 \\ 1 & - 1 \end{array} \right)\) and \(\mathbf { C } = \left( \begin{array} { r r } - 1 & 0 \\ 2 & 1 \end{array} \right)\), where \(a\) is
a constant. a constant.
  1. By multiplying out the matrices on both sides of the equation, verify that \(\mathbf { A } ( \mathbf { B C } ) = ( \mathbf { A B } ) \mathbf { C }\).
  2. State the property of matrix multiplication illustrated by this result.
Question 2:
AnswerMarks Guidance
2(a)  1 a−2 0
A(BC)=
  
−1 2−3 −1
 − 2 − 3 a − a 
=
− 4 − 2
2+a −a−1 0
(AB)C=
  
 0 −2 2 1
 − 2 − 3 a − a 
= [so AB(C) = A(BC)]
AnswerMarks
− 4 − 2B1
B1
B1
B1
AnswerMarks
[4]1.1
1.1
1.1
AnswerMarks
2.2a−2 0
BC=   (BC)
−3 −1
 2 + a − a 
A B =
0 − 2
cao
AnswerMarks Guidance
2(b) Associativity
[1]1.2 
Question 2:
2 | (a) |  1 a−2 0
A(BC)=
  
−1 2−3 −1
 − 2 − 3 a − a 
=
− 4 − 2
2+a −a−1 0
(AB)C=
  
 0 −2 2 1
 − 2 − 3 a − a 
= [so AB(C) = A(BC)]
− 4 − 2 | B1
B1
B1
B1
[4] | 1.1
1.1
1.1
2.2a | −2 0
BC=   (BC)
−3 −1
 2 + a − a 
A B =
0 − 2
cao
2 | (b) | Associativity | B1
[1] | 1.2
2 The matrices $\mathbf { A } , \mathbf { B }$ and $\mathbf { C }$ are given by $\mathbf { A } = \left( \begin{array} { r r } 1 & a \\ - 1 & 2 \end{array} \right) , \mathbf { B } = \left( \begin{array} { r r } 2 & 0 \\ 1 & - 1 \end{array} \right)$ and $\mathbf { C } = \left( \begin{array} { r r } - 1 & 0 \\ 2 & 1 \end{array} \right)$, where $a$ is\\
a constant. a constant.
\begin{enumerate}[label=(\alph*)]
\item By multiplying out the matrices on both sides of the equation, verify that $\mathbf { A } ( \mathbf { B C } ) = ( \mathbf { A B } ) \mathbf { C }$.
\item State the property of matrix multiplication illustrated by this result.
\end{enumerate}

\hfill \mbox{\textit{OCR MEI Further Pure Core AS 2024 Q2 [5]}}
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