November 2021 Paper 1 Q11
11 \(\begin{pmatrix} 2 & 1 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} a & b \\ 0 & 0.4 \end{pmatrix} = k\,\mathbf{I} \qquad\) where \(k\) is a constant and \(\mathbf{I}\) is the identity matrix.
Work out the values of \(a\) and \(b\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\begin{bmatrix} 2a & 2b + 0.4 \\ 0 & 1.2 \end{bmatrix}\) or \(2a = k\) or \(k = 1.2\) or \(2b + 0.4 = 0\) | M1 | oe any 3 terms correct in correct position could be implied from second M mark |
| \(2a = k\) and \(2b + 0.4 = 0\) | M1dep | oe eg \(2a = 1.2\) and \(2b + 0.4 = 0\) |
| \(a = 0.6\) or \(b = -0.2\) | M1 | oe |
| \(a = 0.6\) and \(b = -0.2\) | A1 | oe |