12.
$$\mathbf { M } = \left( \begin{array} { r r r }
2 & - 1 & 1
3 & k & 4
3 & 2 & - 1
\end{array} \right) \quad \text { where } k \text { is a constant }$$
- Find the values of \(k\) for which the matrix \(\mathbf { M }\) has an inverse.
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[2] - Find, in terms of \(p\), the coordinates of the point where the following planes intersect
$$\begin{aligned}
& 2 x - y + z = p
& 3 x - 6 y + 4 z = 1
& 3 x + 2 y - z = 0
\end{aligned}$$ - Find the value of \(q\) for which the set of simultaneous equations
$$\begin{aligned}
& 2 x - y + z = 1
& 3 x - 5 y + 4 z = q
& 3 x + 2 y - z = 0
\end{aligned}$$
can be solved. - For this value of \(q\), interpret the solution of the set of simultaneous equations geometrically.
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