Matrices practice questions

Secondary 4 topics from the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise matrices free

What this topic covers

Worked examples

Example 1

Given matrix C=(6−164−80)C = \begin{pmatrix} 6 & -1 & 6 \\ 4 & -8 & 0 \end{pmatrix}, find the element in the 1st row and 1st column.
Show the worked solution
  • We look for the element in row $1$ and column $1$.
  • Row $1$ of $C$: $\begin{pmatrix} 6 & -1 & 6 \end{pmatrix}$
  • The 1st entry is $6$.
  • So the element in the 1st row and 1st column is $6$.

Answer: 66

Example 2

A factory produces three products using two machines. Let P=(322232)\mathbf{P} = \begin{pmatrix} 3 & 2 \\ 2 & 2 \\ 3 & 2 \end{pmatrix} be the matrix of hours each product spends on each machine, with rows Product X, Product Y, Product Z and columns Machine A, Machine B. Machine A produces 5 units per hour and Machine B produces 8 units per hour, so let Q=(58)\mathbf{Q} = \begin{pmatrix} 5 \\ 8 \end{pmatrix} be the rate matrix. Evaluate PQ\mathbf{PQ} and state the total units produced for Product Y.
Show the worked solution
  • Let $\mathbf{P} = \begin{pmatrix} 3 & 2 \\ 2 & 2 \\ 3 & 2 \end{pmatrix}$ (hours, rows = products, cols = machines)
  • and $\mathbf{Q} = \begin{pmatrix} 5 \\ 8 \end{pmatrix}$ (units per hour for each machine).
  • $\mathbf{PQ} = \begin{pmatrix} 3 & 2 \\ 2 & 2 \\ 3 & 2 \end{pmatrix} \begin{pmatrix} 5 \\ 8 \end{pmatrix}$
  • $= \begin{pmatrix} 3(5) + 2(8) \\ 2(5) + 2(8) \\ 3(5) + 2(8) \end{pmatrix}$
  • $= \begin{pmatrix} 15 + 16 \\ 10 + 16 \\ 15 + 16 \end{pmatrix}$
  • $= \begin{pmatrix} 31 \\ 26 \\ 31 \end{pmatrix}$
  • Theelementinrow2correspondstoProductY.The element in row 2 corresponds to Product Y.
  • Total units produced for Product Y $= 26$ units.

Answer: 2626

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

Other Secondary 4 topics