5.
$$\mathbf { M } = \left( \begin{array} { r r r }
4 & - 5 & 0
k & 2 & 0
- 3 & - 5 & k
\end{array} \right) \text {, where } k \text { is a real constant, } k \neq 0 , k \neq - \frac { 8 } { 5 }$$
- Find, in terms of \(k\), the inverse of the matrix \(\mathbf { M }\).
A transformation \(T : \mathbb { R } ^ { 3 } \rightarrow \mathbb { R } ^ { 3 }\) is represented by the matrix
$$\left( \begin{array} { r r r }
4 & - 5 & 0
- 1 & 2 & 0
- 3 & - 5 & - 1
\end{array} \right)$$
The transformation \(T\) maps the plane \(\Pi _ { 1 }\) onto the plane \(\Pi _ { 2 }\)
Given that the plane \(\Pi _ { 2 }\) has equation \(2 x - z = 4\) - find a cartesian equation of the plane \(\Pi _ { 1 }\)