Standard +0.3 This is a straightforward application of the invariant line condition for a 2×2 matrix. Students need to apply the condition that points on y=mx map to points on the same line, leading to a simple quadratic equation in m. While it requires understanding the concept of invariant lines, the algebraic manipulation is routine for Further Maths students.
6 Given that \(y = m x\) is an invariant line of the transformation with matrix \(\left( \begin{array} { r r } 1 & 2 \\ 2 & - 2 \end{array} \right)\), determine the possible values of \(m\).
Section B (113 marks)
Answer all the questions.
substituting y = m x and 2 x − 2 y = m ( x + 2 y )
2 x − 2 m x = m ( x + 2 m x )
2 m 2 + 3 m − 2 = 0
Answer
Marks
m = − 2 , 12
M1
M1
A1
A1
Answer
Marks
[4]
1.1
2.1
1.1
Answer
Marks
2.2a
Could see mx instead of y in the initial
matrix multiplication for this mark
Question 6:
6 | (1 2)(x) ( x+2y)
=
2 −2 y 2x−2y
substituting y = m x and 2 x − 2 y = m ( x + 2 y )
2 x − 2 m x = m ( x + 2 m x )
2 m 2 + 3 m − 2 = 0
m = − 2 , 12 | M1
M1
A1
A1
[4] | 1.1
2.1
1.1
2.2a | Could see mx instead of y in the initial
matrix multiplication for this mark
6 Given that $y = m x$ is an invariant line of the transformation with matrix $\left( \begin{array} { r r } 1 & 2 \\ 2 & - 2 \end{array} \right)$, determine the possible values of $m$.
Section B (113 marks)\\
Answer all the questions.
\hfill \mbox{\textit{OCR MEI Further Pure Core 2021 Q6 [4]}}