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Matrices Practice Problems with Solutions - IGCSE Year 11

IGCSE Year 11 | Math | Matrices
Name: _________________________ Date: _________________________ Score: _______ / 40

The matrix [1 2; 3 4] has order 2 × 2, and two matrices can be added only when they have the same order, so this Year 11 sheet opens with orders and the addition rule. Multiplication needs columns of A to equal rows of B in the key.

Key Takeaways

Section A: Multiple Choice Questions (1 Mark Each)

Choose the correct option for each question.
1. The order of the matrix [1 2; 3 4] is
(a) 2 × 1(b) 2 × 2(c) 1 × 2(d) 3 × 3
2. Two matrices can be added together if they have
(a) The same number of rows(b) The same order(c) The same elements(d) Any order
3. The product AB of two matrices A and B is defined when
(a) m = p(b) The number of columns of A equals the number of rows of B(c) m = n(d) n = p
4. The transpose of the matrix [1 2; 3 4] is
(a) [1 3; 2 4](b) [4 3; 2 1](c) [1 2; 3 4](d) [2 1; 4 3]
5. A matrix in which every element is zero is called a
(a) Identity matrix(b) Zero matrix(c) Square matrix(d) Column matrix
6. The sum of the matrices [1 2; 3 4] and [1 1; 1 1] is
(a) [2 3; 4 5](b) [2 3; 4 4](c) [1 2; 3 4](d) [2 2; 4 4]

Section B: Short Answer Type Questions (2 Marks Each)

Show all steps clearly.
7. Write the order of the matrix [a b c].
8. When can two matrices be added together?
9. Write the transpose of the matrix [1 2; 3 4].
10. Write the condition for the product AB to be defined.
11. Write the zero matrix of order 2 × 2.
12. What is the order of the identity matrix I₂?
13. Find [1 2] + [3 4].
14. Write the element in the second row, first column of the matrix [1 2; 3 4].

Section C: Numericals & Word Problems (3 Marks Each)

Apply the concepts to solve the problems. Show all working.
15. A = [1 2; 3 4] and B = [5 6; 7 8]. Find A + B.
16. Find 2 × [1 2; 3 4].
17. A shop's Monday sales are (10, 5) and Tuesday sales are (12, 7), written as row matrices. Find the total sales over the two days.
18. A = [5 6; 7 8] and B = [1 2; 3 4]. Find A - B.
19. If A = [1 2; 3 4], write Aᵀ and state the order of Aᵀ.
20. The matrices [x 2] and [3 4] are equal. Find the value of x.

Answer Key

1. b) 2 × 2
2. b) The same order
3. b) The number of columns of A equals the number of rows of B
4. a) [1 3; 2 4]
5. b) Zero matrix
6. a) [2 3; 4 5]
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet

People Also Ask

What is the order of the matrix [1 2; 3 4]?

2 × 2, option (b) in this worksheet (Q1).

When can two matrices be added?

When they have the same order, option (b) in this worksheet (Q2).

When can two matrices be multiplied?

When the columns of A equal the rows of B, option (b) in this worksheet (Q3).

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