6.
$$\mathbf { A } = \left( \begin{array} { r r r }
1 & - 1 & 1
1 & 1 & 1
1 & 2 & a
\end{array} \right) \quad a \neq 1$$
- Find \(\mathbf { A } ^ { - 1 }\) in terms of \(a\).
.
The straight line \(l _ { 1 }\) is mapped onto the straight line \(l _ { 2 }\) by the transformation represented by the matrix \(\mathbf { B }\).
$$\mathbf { B } = \left( \begin{array} { r r r }
1 & - 1 & 1
1 & 1 & 1
1 & 2 & 4
\end{array} \right)$$
The equation of \(l _ { 2 }\) is
$$( \mathbf { r } - ( 12 \mathbf { i } + 4 \mathbf { j } + 6 \mathbf { k } ) ) \times ( - 6 \mathbf { i } + 2 \mathbf { j } + 3 \mathbf { k } ) = \mathbf { 0 }$$ - Find a vector equation for the line \(l _ { 1 }\)