## Exam-Style Question on Matrices## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 31. This question is similar to one that appeared on an IB Standard paper in 2013. The use of a calculator is allowed.

If the equations below can be represented as the matrix equation \(AX=B\), where \(X=\begin{pmatrix}x\\y\\z\end{pmatrix}\)

$$x-2y-z=2$$ $$x+y=1$$ $$-2x+y-3z=-23$$(a) What is the matrix \(A\) ?

(b) What is the matrix \(B\) ?

(c) Find the matrix \(A^{-1}\).

(d) Use your answers to the previous three parts of this question to find the values of \(x,y\) and \(z\).

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