Let $A=\begin{pmatrix}1&2&k\0&1&3\4&0&1\end{pmatrix}$ and $B=\begin{pmatrix}5\k+2\9\end{pmatrix}$. Find the integer value of $k$ for which the system $AX=B$ has a unique solution and that solution consists entirely of integers. Then give the solution vector $X$.

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k=5; \;X=\begin{pmatrix}0\-20\9\end{pmatrix}

Gce Model Questions Vol1 2017 Further Mathematics Question 40

Let \(A=\begin{pmatrix}1&2&k\\0&1&3\\4&0&1\end{pmatrix}\) and \(B=\begin{pmatrix}5\\k+2\\9\end{pmatrix}\). Find the integer value of \(k\) for which the system \(AX=B\) has a unique solution and that solution consists entirely of integers. Then give the solution vector \(X\).

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