|
|
Exam-Style Question on MatricesA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 787. This question is typical of the type of question in an IB Standard examination. The use of a calculator is allowed.
A furniture shop sells four items: chairs, beds, stools and tables. Over one week the manager recorded how many of each item were sold on each weekday. The data are arranged in the \(5 \times 4\) matrix \(A\) where rows correspond to Monday, Tuesday, Wednesday, Thursday and Friday in that order, and the columns are chairs, beds, stools, tables in that order.
$$ A \;=\; \begin{bmatrix} 6 & 2 & 5 & 3 \\ 4 & 1 & 3 & 2 \\ 7 & 3 & 4 & 4 \\ 5 & 2 & 2 & 1 \\ 9 & 4 & 6 & 5 \end{bmatrix} $$
The prices of the four items, in British pounds, are stored in the \(4 \times 1\) column matrix \(P\) below, using the same item order as the columns of \(A\).
$$ P \;=\; \begin{bmatrix} 55 \\[2pt] 420 \\[2pt] 30 \\[2pt] 160 \end{bmatrix} \qquad\text{(entries are in pounds)} $$
(a) By performing the matrix multiplication \(T = A P\), find the \(5 \times 1\) matrix \(T\) that gives the total amount taken, in pounds, on each weekday. State clearly which row of \(T\) corresponds to which day.
(b) Use your result for \(T\) to identify the weekday with the greatest takings.
(c) Hence find the total amount taken for the whole week.
|
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription. Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves. This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures. A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience. |
|
Drag this panel down to reveal the solution
If you need more practice try the self-checking interactive exercises called Matrix Multiplication.
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
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 - 2025 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/
