# Exam-Style Questions on Matrices

## Problems on Matrices adapted from questions set in previous Mathematics 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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