Sec 4 E-Math · Matrices

Interpreting matrices questions with answers

Practice questions on interpreting matrices, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

The matrix $P = \begin{pmatrix} 3 & 9 & 13 \\ 10 & 7 & 5 \end{pmatrix}$ shows the numbers of small, medium and large cups of juice sold at Stall A and Stall B (one row for each stall). The matrix $Q = \begin{pmatrix} 1.5 \\ 2 \\ 2.5 \end{pmatrix}$ shows the prices, in dollars, of a small, medium and large cup. Find $PQ$ .

Step 1 of 4

The order of PQ

(2 \times 3)(3 \times 1) \rightarrow 2 \times 1

PQ = \begin{pmatrix} 3 & 9 & 13 \\ 10 & 7 & 5 \end{pmatrix}\begin{pmatrix} 1.5 \\ 2 \\ 2.5 \end{pmatrix}

Try a question: Interpreting matrices

Free · no sign-up

Answer a real practice question. Get it wrong and MugCorner shows you where it went wrong, with hints and a step-by-step guide.

Questions

Question 1Find PQ in context
The matrix $P = \begin{pmatrix} 9 & 3 & 8 \\ 10 & 13 & 5 \end{pmatrix}$ shows the numbers of adult, child and senior tickets sold on Friday and Saturday (one row for each day). The matrix $Q = \begin{pmatrix} 12 \\ 8 \\ 6 \end{pmatrix}$ shows the prices, in dollars, of an adult, child and senior ticket. Find $PQ$ .
Show the worked solution
1. Step 1: The order of PQ $(2 \times 3)(3 \times 1) \rightarrow 2 \times 1$ $PQ = \begin{pmatrix} 9 & 3 & 8 \\ 10 & 13 & 5 \end{pmatrix}\begin{pmatrix} 12 \\ 8 \\ 6 \end{pmatrix}$
2. Step 2: Row 1: Friday $9 \times 12 + 3 \times 8 + 8 \times 6 = 180$
3. Step 3: Row 2: Saturday $10 \times 12 + 13 \times 8 + 5 \times 6 = 254$
4. Step 4: Write the answer as a matrix $PQ = \begin{pmatrix} 180 \\ 254 \end{pmatrix}$
Question 2Find PQ in context
The matrix $P = \begin{pmatrix} 8 & 14 & 7 \\ 6 & 12 & 5 \end{pmatrix}$ shows the numbers of wins, draws and losses for the Lions and the Tigers in a league (one row for each team). The matrix $Q = \begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix}$ shows the points given for a win, a draw and a loss. Find $PQ$ .
Show the worked solution
1. Step 1: The order of PQ $(2 \times 3)(3 \times 1) \rightarrow 2 \times 1$ $PQ = \begin{pmatrix} 8 & 14 & 7 \\ 6 & 12 & 5 \end{pmatrix}\begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix}$
2. Step 2: Row 1: the Lions $8 \times 3 + 14 \times 1 + 7 \times 0 = 38$
3. Step 3: Row 2: the Tigers $6 \times 3 + 12 \times 1 + 5 \times 0 = 30$
4. Step 4: Write the answer as a matrix $PQ = \begin{pmatrix} 38 \\ 30 \end{pmatrix}$
Question 3What an element represents
The matrix $P = \begin{pmatrix} 15 & 12 \\ 11 & 9 \end{pmatrix}$ shows the numbers of loaves and buns sold by a bakery on Monday and Tuesday (one row for each day). The matrix $Q = \begin{pmatrix} 3.5 \\ 1.2 \end{pmatrix}$ shows the prices, in dollars, of a loaf and a bun. Which of the following does the element in the second row of $PQ$ represent? (A) the number of buns sold over these days; (B) the price of a loaf; (C) the number of loaves and buns sold on Tuesday; (D) the total amount, in dollars, the bakery collected on Tuesday.
Show the worked solution
1. Step 1: Row 2 of PQ uses row 2 of P: Tuesday $11 \times 3.5 + 9 \times 1.2 = 49.3$
2. Step 2: What do you get when each number in that row is multiplied by its price and added?So it is the total amount, in dollars, the bakery collected on Tuesday: option D.
Question 4What an element represents
The matrix $P = \begin{pmatrix} 14 & 12 & 5 \\ 5 & 14 & 6 \end{pmatrix}$ shows the numbers of questions answered correctly, answered wrongly and left unanswered by Hui Min and Ravi in a quiz (one row for each student). The matrix $Q = \begin{pmatrix} 4 \\ -1 \\ 0 \end{pmatrix}$ shows the marks given for a correct answer, a wrong answer and an unanswered question. Which of the following does the element in the second row of $PQ$ represent? (A) the number of correct answers given by Ravi; (B) the mark for a correct answer; (C) the total quiz score of Ravi; (D) the number of questions answered by Ravi.
Show the worked solution
1. Step 1: Row 2 of PQ uses row 2 of P: Ravi $5 \times 4 + 14 \times (-1) + 6 \times 0 = 6$
2. Step 2: What do you get when each number in that row is multiplied by its value and added?So it is the total quiz score of Ravi: option C.
Question 5A total from PQ
The matrix $P = \begin{pmatrix} 5 & 11 \\ 6 & 8 \end{pmatrix}$ shows the numbers of loaves and buns sold by a bakery on Monday and Tuesday (one row for each day). The matrix $Q = \begin{pmatrix} 3.5 \\ 1.2 \end{pmatrix}$ shows the prices, in dollars, of a loaf and a bun. Using $PQ$ , find the total amount, in dollars, the bakery collected over these days.
Show the worked solution
1. Step 1: Find PQ: each row of P times the column Q $PQ = \begin{pmatrix} 30.7 \\[8pt] 30.6 \end{pmatrix}$
2. Step 2: Add its elements $\text{Total} = 61.3$
Question 6A total from PQ
The matrix $P = \begin{pmatrix} 3 & 3 & 15 \\ 5 & 3 & 7 \end{pmatrix}$ shows the numbers of small, medium and large cups of juice sold at Stall A and Stall B (one row for each stall). The matrix $Q = \begin{pmatrix} 1.5 \\ 2 \\ 2.5 \end{pmatrix}$ shows the prices, in dollars, of a small, medium and large cup. Using $PQ$ , find the total amount, in dollars, collected at all the stalls.
Show the worked solution
1. Step 1: Find PQ: each row of P times the column Q $PQ = \begin{pmatrix} 48 \\[8pt] 31 \end{pmatrix}$
2. Step 2: Add its elements $\text{Total} = 79$

More on matrices

Notes: Matrices Worksheet with answers (PDF)

Endless questions on interpreting matrices

A free account gives you new questions every time, step-by-step help, and tracks what you've mastered.

Start free

Worked example

The matrix

P = \begin{pmatrix} 3 & 9 & 13 \\ 10 & 7 & 5 \end{pmatrix}

shows the numbers of small, medium and large cups of juice sold at Stall A and Stall B (one row for each stall). The matrix

Q = \begin{pmatrix} 1.5 \\ 2 \\ 2.5 \end{pmatrix}

shows the prices, in dollars, of a small, medium and large cup. Find

PQ

Step 1 of 4

The order of PQ

(2 \times 3)(3 \times 1) \rightarrow 2 \times 1

PQ = \begin{pmatrix} 3 & 9 & 13 \\ 10 & 7 & 5 \end{pmatrix}\begin{pmatrix} 1.5 \\ 2 \\ 2.5 \end{pmatrix}

Questions

Question 1Find PQ in context

The matrix $P = \begin{pmatrix} 9 & 3 & 8 \\ 10 & 13 & 5 \end{pmatrix}$ shows the numbers of adult, child and senior tickets sold on Friday and Saturday (one row for each day). The matrix $Q = \begin{pmatrix} 12 \\ 8 \\ 6 \end{pmatrix}$ shows the prices, in dollars, of an adult, child and senior ticket. Find $PQ$ .

Show the worked solution

Step 1: The order of PQ $(2 \times 3)(3 \times 1) \rightarrow 2 \times 1$ $PQ = \begin{pmatrix} 9 & 3 & 8 \\ 10 & 13 & 5 \end{pmatrix}\begin{pmatrix} 12 \\ 8 \\ 6 \end{pmatrix}$
Step 2: Row 1: Friday $9 \times 12 + 3 \times 8 + 8 \times 6 = 180$
Step 3: Row 2: Saturday $10 \times 12 + 13 \times 8 + 5 \times 6 = 254$
Step 4: Write the answer as a matrix $PQ = \begin{pmatrix} 180 \\ 254 \end{pmatrix}$

Question 2Find PQ in context

The matrix $P = \begin{pmatrix} 8 & 14 & 7 \\ 6 & 12 & 5 \end{pmatrix}$ shows the numbers of wins, draws and losses for the Lions and the Tigers in a league (one row for each team). The matrix $Q = \begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix}$ shows the points given for a win, a draw and a loss. Find $PQ$ .

Show the worked solution

Step 1: The order of PQ $(2 \times 3)(3 \times 1) \rightarrow 2 \times 1$ $PQ = \begin{pmatrix} 8 & 14 & 7 \\ 6 & 12 & 5 \end{pmatrix}\begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix}$
Step 2: Row 1: the Lions $8 \times 3 + 14 \times 1 + 7 \times 0 = 38$
Step 3: Row 2: the Tigers $6 \times 3 + 12 \times 1 + 5 \times 0 = 30$
Step 4: Write the answer as a matrix $PQ = \begin{pmatrix} 38 \\ 30 \end{pmatrix}$

Question 3What an element represents

The matrix $P = \begin{pmatrix} 15 & 12 \\ 11 & 9 \end{pmatrix}$ shows the numbers of loaves and buns sold by a bakery on Monday and Tuesday (one row for each day). The matrix $Q = \begin{pmatrix} 3.5 \\ 1.2 \end{pmatrix}$ shows the prices, in dollars, of a loaf and a bun. Which of the following does the element in the second row of $PQ$ represent? (A) the number of buns sold over these days; (B) the price of a loaf; (C) the number of loaves and buns sold on Tuesday; (D) the total amount, in dollars, the bakery collected on Tuesday.

Show the worked solution

Step 1: Row 2 of PQ uses row 2 of P: Tuesday $11 \times 3.5 + 9 \times 1.2 = 49.3$
Step 2: What do you get when each number in that row is multiplied by its price and added?So it is the total amount, in dollars, the bakery collected on Tuesday: option D.

Question 4What an element represents

The matrix $P = \begin{pmatrix} 14 & 12 & 5 \\ 5 & 14 & 6 \end{pmatrix}$ shows the numbers of questions answered correctly, answered wrongly and left unanswered by Hui Min and Ravi in a quiz (one row for each student). The matrix $Q = \begin{pmatrix} 4 \\ -1 \\ 0 \end{pmatrix}$ shows the marks given for a correct answer, a wrong answer and an unanswered question. Which of the following does the element in the second row of $PQ$ represent? (A) the number of correct answers given by Ravi; (B) the mark for a correct answer; (C) the total quiz score of Ravi; (D) the number of questions answered by Ravi.

Show the worked solution

Step 1: Row 2 of PQ uses row 2 of P: Ravi $5 \times 4 + 14 \times (-1) + 6 \times 0 = 6$
Step 2: What do you get when each number in that row is multiplied by its value and added?So it is the total quiz score of Ravi: option C.

Question 5A total from PQ

The matrix $P = \begin{pmatrix} 5 & 11 \\ 6 & 8 \end{pmatrix}$ shows the numbers of loaves and buns sold by a bakery on Monday and Tuesday (one row for each day). The matrix $Q = \begin{pmatrix} 3.5 \\ 1.2 \end{pmatrix}$ shows the prices, in dollars, of a loaf and a bun. Using $PQ$ , find the total amount, in dollars, the bakery collected over these days.

Show the worked solution

Step 1: Find PQ: each row of P times the column Q $PQ = \begin{pmatrix} 30.7 \\[8pt] 30.6 \end{pmatrix}$
Step 2: Add its elements $\text{Total} = 61.3$

Question 6A total from PQ

The matrix $P = \begin{pmatrix} 3 & 3 & 15 \\ 5 & 3 & 7 \end{pmatrix}$ shows the numbers of small, medium and large cups of juice sold at Stall A and Stall B (one row for each stall). The matrix $Q = \begin{pmatrix} 1.5 \\ 2 \\ 2.5 \end{pmatrix}$ shows the prices, in dollars, of a small, medium and large cup. Using $PQ$ , find the total amount, in dollars, collected at all the stalls.

Show the worked solution

Step 1: Find PQ: each row of P times the column Q $PQ = \begin{pmatrix} 48 \\[8pt] 31 \end{pmatrix}$
Step 2: Add its elements $\text{Total} = 79$