Specimen 2020 Paper 2 Q6

AQACurrent spec4 marksMatrices

6 \(\mathbf{A} = \begin{pmatrix} 4 & -1 \\ -7 & 2 \end{pmatrix} \qquad \mathbf{B} = \begin{pmatrix} s \\ -5 \end{pmatrix} \qquad \mathbf{C} = \begin{pmatrix} -1 \\ t \end{pmatrix} \qquad \mathbf{D} = \begin{pmatrix} 2 & 1 \\ 7 & u \end{pmatrix}\)

\(s\), \(t\) and \(u\) are constants.

(a) \(\mathbf{AB} = \mathbf{C}\)

Work out the values of \(s\) and \(t\). [3 marks]

(b) \(\mathbf{AD} = \mathbf{I}\)

Work out the value of \(u\). [1 mark]