19.
$$\mathbf { A } = \left( \begin{array} { r r r }
3 & 1 & - 1
1 & 1 & 1
5 & 3 & u
\end{array} \right) , \quad u \neq 1$$
- Show that \(\operatorname { det } \mathbf { A } = 2 ( u - 1 )\).
- Find the inverse of \(\mathbf { A }\).
The image of the vector \(\left( \begin{array} { l } a
b
c \end{array} \right)\) when transformed by the matrix \(\left( \begin{array} { r r r } 3 & 1 & - 1
1 & 1 & 1
5 & 3 & 6 \end{array} \right)\) is \(\left( \begin{array} { l } 3
1
6 \end{array} \right)\). - Find the values of \(a , b\) and \(c\).
(3)
[0pt]
[P6 June 2003 Qn 6]