Let $A=\begin{pmatrix}k&2&-1\3&k&4\5&-2&k\end{pmatrix}.$\n(a) Find all values of $k$ for which $A$ is invertible.\n(b) For $k=2$, compute $\det A$ and solve the system $A\mathbf{x}=\begin{pmatrix}1\0\3\end{pmatrix}.$

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Accepted Answer

determinant = 68; solution = (21/34, -19/68, -11/34)

Neco 2017 Further Mathematics Question 28

Let \(A=\begin{pmatrix}k&2&-1\\3&k&4\\5&-2&k\end{pmatrix}.\)\n(a) Find all values of \(k\) for which \(A\) is invertible.\n(b) For \(k=2\), compute \(\det A\) and solve the system \(A\mathbf{x}=\begin{pmatrix}1\\0\\3\end{pmatrix}.\)

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