June 2024 Paper 2 Q5
5
(a) \[\begin{pmatrix} c & 1 \\ 5d & 3 \end{pmatrix}\begin{pmatrix} -2 & 0 \\ 7 & 3 \end{pmatrix} = \begin{pmatrix} -5 & 3 \\ 0 & 9 \end{pmatrix}\]
Work out the values of \(c\) and \(d\). [3 marks]
(b) \[\begin{pmatrix} 5 & 2 \\ 1 & 4 \end{pmatrix}\mathbf{M} = \begin{pmatrix} 5 & 2 \\ 1 & 4 \end{pmatrix}\]
Write down matrix M [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| \(-2c + 7\) and \(-10d + 21\) or \(-2c + 7 = -5\) or \(-10d + 21 = 0\) | M1 | oe the two expressions may be seen in a matrix or embedded in two equations |
| \(c = 6\) | A1 | |
| \(d = \dfrac{21}{10}\) or \(d = 2.1\) | A1 | oe value |
Additional guidance
| Ignore simplification or conversion attempt after correct answer seen for \(d\) eg \(d = \dfrac{-21}{-10}\) in working with \(d = -2.1\) on answer line | 2nd A1 |
| The two expressions may be seen in an incorrect matrix or two incorrect equations eg1 \(\begin{pmatrix} -2c + 7 & -10d + 21 \\ 2 & 9 \end{pmatrix}\) | M1 |
| eg2 \(-2c + 7 = 3\) and \(-10d + 21 = 9\) | M1 |
| A correct equation is not implied by a matrix equation eg \(\begin{pmatrix} -2c + 7 & 3 \\ 10d + 10 & 9 \end{pmatrix} = \begin{pmatrix} -5 & 3 \\ 0 & 9 \end{pmatrix}\) | M0 |
| Answer | Mark | Comments |
|---|---|---|
| \(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\) | B1 | do not accept I or identity unless the correct 2 by 2 matrix is also seen |