10 The matrix \(\mathbf { M }\) is defined as
$$\mathbf { M } = \left[ \begin{array} { c c c }
2 & - 1 & 1
- 1 & - 1 & - 2
1 & 2 & c
\end{array} \right]$$
where \(c\) is a real number.
10
- The linear transformation T is represented by the matrix \(\mathbf { M }\)
Show that, for one particular value of \(c\), the image under \(T\) of every point lies in the plane
$$x + 5 y + 3 z = 0$$
State the value of \(c\) for which this occurs.
10 - It is given that \(\mathbf { M }\) is a non-singular matrix.
10 - State any restrictions on the value of \(c\)
10- (iii) Using your answer from part (b)(ii), solve \(\begin{array} { r } 2 x - y + z = - 3
|
| - x - y - 2 z = - 6 |
| x + 2 y + 4 z = 13 \end{array}\) | \(\_\_\_\_\) |