Easy -1.2 This is a straightforward FP1 question requiring only basic matrix arithmetic (scalar multiplication and addition) and solving two simple simultaneous equations. The diagonal structure makes it trivial as each entry gives an independent equation. No conceptual difficulty or problem-solving insight required.
2 The matrices \(\mathbf { A }\) and \(\mathbf { B }\) are given by \(\mathbf { A } = \left( \begin{array} { l l } 3 & 0 \\ 0 & 1 \end{array} \right)\) and \(\mathbf { B } = \left( \begin{array} { l l } 5 & 0 \\ 0 & 2 \end{array} \right)\) and \(\mathbf { I }\) is the \(2 \times 2\) identity matrix. Find the values of the constants \(a\) and \(b\) for which \(a \mathbf { A } + b \mathbf { B } = \mathbf { I }\).
2 The matrices $\mathbf { A }$ and $\mathbf { B }$ are given by $\mathbf { A } = \left( \begin{array} { l l } 3 & 0 \\ 0 & 1 \end{array} \right)$ and $\mathbf { B } = \left( \begin{array} { l l } 5 & 0 \\ 0 & 2 \end{array} \right)$ and $\mathbf { I }$ is the $2 \times 2$ identity matrix. Find the values of the constants $a$ and $b$ for which $a \mathbf { A } + b \mathbf { B } = \mathbf { I }$.
\hfill \mbox{\textit{OCR FP1 2009 Q2 [4]}}