3 Matrices \(\mathbf { A }\) and \(\mathbf { B }\) are given by \(\mathbf { A } = \left( \begin{array} { r r } 4 & - 3
- 2 & 2 \end{array} \right)\) and \(\mathbf { B } = \left( \begin{array} { r r } 3 & - 5
0 & 1 \end{array} \right)\).
- Find 2A - 4B.
- Write down the matrix \(\mathbf { C }\) such that \(\mathbf { A C } = 2 \mathbf { A }\).
- Find the value of \(\operatorname { det } \mathbf { A }\).
- In this question you must show detailed reasoning.
Use \(\mathbf { A } ^ { - 1 }\) to solve the equations \(4 \mathrm { x } - 3 \mathrm { y } = 7\) and \(- 2 \mathrm { x } + 2 \mathrm { y } = 9\).