Solving equations using matrices — KCSE Mathematics

KCSE Mathematics · 106 practice questions · 3 syllabus objectives

34 easy39 medium33 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Express a system of two simultaneous linear equations in matrix form AX = B

Solve the matrix equation AX = B using X = A⁻¹B when the inverse of A exists

Solving equations using matrices

Sample Questions

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1
easySHORT ANSWER4 marks

State the steps to obtain the solution for the matrix equation AX = B where A = [[2, 1], [3, 4]] and B = [[5], [6]]. (4 marks)

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Part (a) — 4 marks
Calculate the determinant of A (1 mk)
Find the inverse A⁻¹ of matrix A (1 mk)
Multiply A⁻¹ by B to find X (1 mk)
State the values of x and y from X (1 mk)
2
easySHORT ANSWER3 marks

Identify the inverse of the matrix A = [[1, 2], [3, 4]]. (3 marks)

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Part (a) — 3 marks
det(A) = -2 (1 mk)
A⁻¹ = [[-2, 1], [1.5, -0.5]] (1 mk)
Correctly stated steps to find A⁻¹ (1 mk)
3
easySHORT ANSWER4 marks

Consider the equations 5x + 2y = 20 and 3x + 4y = 18. Express them in the matrix form AX = B and determine the inverse of A. (4 marks)

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Part (a) — 2 marks
A = [[5, 2], [3, 4]] (1 mk)
X = [x, y]ᵀ (1 mk)
B = [20, 18]ᵀ (0 mks)
Part (b) — 2 marks
A⁻¹ = [[0.4, -0.2], [-0.3, 0.5]] (2 mks)
4

If A = [[1, 2], [3, 4]] and B = [5, 6]ᵀ, find A⁻¹ and use it to solve for X in the equation AX = B. (4 marks)

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