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Year 11 Matrix Operations

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Year 11 Matrix Operations

For matrix calculations, show your working and write each answer as a matrix. Matrix dimensions are given as rows × columns. Calculators are not required.

Addition and subtraction

1.Let A = [[4, −2], [1, 5]] and B = [[3, 6], [−4, 2]]. Find A + B.

2.For C = [[8, 1], [−3, 7]] and D = [[5, −2], [4, 3]], calculate C − D.

3.Which pair of matrices can be added?

A 2 × 3 matrix and a 3 × 2 matrix
A 3 × 2 matrix and a 3 × 2 matrix
A 1 × 4 matrix and a 4 × 1 matrix
A 2 × 2 matrix and a 2 × 3 matrix

4.Evaluate [[6, −1], [2, 3]] + [[−2, 4], [5, −6]] − [[1, 2], [−3, 4]].

Multiplication and dimensions

5.Calculate MN for M = [[1, 3], [−2, 4]] and N = [[5], [−1]].

6.Find the product RS where R = [[2, −1, 4]] and S = [[3], [0], [−2]].

7.Which multiplication is not defined?

(3 × 2)(2 × 1)
(2 × 4)(4 × 3)
(2 × 3)(4 × 1)
(1 × 5)(5 × 2)

8.Work out [[2, 1], [−1, 3]] × [[4, −2], [5, 1]].

9.Match each matrix operation to the dimensions of its result. (i) A is 2 × 3 and B is 3 × 4: AB. (ii) C is 4 × 1 and D is 1 × 2: CD. (iii) E and F are both 3 × 2: E + F. (iv) G is 1 × 3 and H is 3 × 1: GH.

(i) AB
(ii) CD
(iii) E + F
(iv) GH

4 × 2
2 × 4
3 × 2
1 × 1

Apply and combine operations

10.A warehouse records stock as [rows: depot; columns: crates of tea, crates of coffee]. On Monday its stock matrix is [[32, 18], [25, 21]], and on Tuesday it is [[27, 24], [31, 16]]. Find the combined stock recorded across both days.

11.Let X = [[3, −2], [1, 4]] and Y = [[−1, 5], [2, 0]]. Calculate (a) X + Y, (b) X − Y, and (c) XY.

12.Let P = [[2, 1, −3], [0, 4, 2]] and Q = [[1, 2], [−2, 3], [5, 0]]. Calculate PQ and state the dimensions of your answer.