# 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 $$z$$.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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