Transum Software

Exam-Style Questions on Matrices

Problems on Matrices adapted from questions set in previous Mathematics exams.


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 \(AX=B\)


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 \(z\).

If you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.

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.

The solutions to the questions on this website are only available to those who have a Transum Subscription.


Exam-Style Questions Main Page


Search for exam-style questions containing a particular word or phrase:

To search the entire Transum website use the search box in the grey area below.


Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


©1997-2023 WWW.TRANSUM.ORG