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Matrices Operations Worksheet

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Matrices Operations Worksheet

A community sports centre is organising equipment and tracking sales. Work through the matrix challenges. For addition and subtraction, matrices must have the same dimensions. For multiplication, the number of columns in the first matrix must equal the number of rows in the second matrix.

Add and subtract

The sports centre counts equipment by location. Each row is a location and each column is a type of equipment.

1.The centre receives the equipment in Matrix B. Calculate A + B to find the new equipment counts at each location.

2.Compare the equipment counts in Matrix A with those in Matrix B. Calculate A − B. What does the top-right entry of your answer represent?

3.The centre orders three identical sets of the equipment listed in Matrix A. Find 3A.

Multiply and check dimensions

A weekend event packs equipment into kits. Use matrix multiplication to combine the quantities.

4.Calculate DC. The rows of D are the two event days, and the columns of C are balls, cones and bibs. State what the first row of your answer tells you.

5.A volunteer proposes multiplying C (a 2 × 3 matrix) by D (a 2 × 2 matrix). Is CD defined? Explain using the inside dimensions.

6.Which product is defined: a 2 × 3 matrix multiplied by a 3 × 1 matrix, or a 2 × 3 matrix multiplied by a 2 × 1 matrix? Choose one and state the dimensions of its result.

2 × 3 multiplied by 3 × 1; result is 2 × 1
2 × 3 multiplied by 2 × 1; result is 2 × 1
Both products are defined
Neither product is defined

Sales and reasoning

The centre sells event packs at its weekend stall. Rows show Saturday and Sunday; columns show small and large packs.

7.Sales increased by 2 small packs and 4 large packs on each day. Write this increase as a 2 × 2 matrix and calculate the new sales matrix.

8.A small pack costs $8 and a large pack costs $15. Represent the prices as a 2 × 1 column matrix in the order small, large. Multiply the sales matrix E by this price matrix to find the takings for each day.

9.True or false: For matrices A and B of the same dimensions, A + B always has the same dimensions as A. Give a short reason.

TrueFalse

10.The centre has a 2 × 3 matrix of daily stock and a 3 × 2 matrix of kit requirements. What are the dimensions of their product, if the multiplication is possible? Explain how you know.