\mathbf{M}=\left(\begin{array}{rrr} 2 & -1 & 1 \\ 3 & k & 4 \\ 3 & 2 & -1 \end{array}\right) where k is a constant (a) Find the values of k for which the matrix M has an inverse. (b) Find, in terms of p, the coordinates of the point where the following planes intersect 2x - y + z = p Зх — бу + 4z — 1 Зх + 2у — z =0 (c) (i) Find the value of q for which the set of simultaneous equations 2x - y + z = 1 3x – 5y + 4z = q Зх + 2у — z= 0 can be solved. (ii) For this value of q, interpret the solution of the set of simultaneous equations geometrically.

Solved: \mathbf{M}=\left(\begin{array}{rrr} 2 & -1 & 1 \\ 3 & k & 4 \\ 3 & 2

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mathbfmleftbeginarrayrrr 2 1 1 3 k 4 3 2 1 endarrayright where k is a

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\mathbf{M}=\left(\begin{array}{rrr} 2 & -1 & 1 \\ 3 & k & 4 \\ 3 & 2 & -1 \end{array}\right) where k is a constant (a) Find the values of k for which the matrix M has an inverse. (b) Find, in terms of p, the coordinates of the point where the following planes intersect 2x - y + z = p Зх — бу + 4z — 1 Зх + 2у — z =0 (c