## Exam-Style Questions on Matrices## Problems on Matrices adapted from questions set in previous exams. |

## 1. | IB Standard |

Let \(A\) = \( \begin{pmatrix} 1 & 3 & 2 \\ 3 & 0 & 1 \\ 1 & 1 & 2 \\ \end{pmatrix} \) and \(B\) = \( \begin{pmatrix} 7 \\ 7 \\ 5 \\ \end{pmatrix} \)

(a) Write down \(A^{-1}\)

(b) Find \(X\) if \(AX=B\)

## 2. | IB Standard |

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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