Matrices (addition, multiplication, determinants) — KCSE Mathematics

KCSE Mathematics · 127 practice questions · 4 syllabus objectives

45 easy43 medium39 hard

What You'll Learn

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

Add and subtract matrices of the same order and multiply a matrix by a scalar

Multiply two compatible matrices (m×n by n×p) and state when multiplication is defined and commutative

Calculate the determinant and inverse of a 2×2 matrix; state the condition for the inverse to exist (det ≠ 0)

Matrices (addition, multiplication, determinants)

Sample Questions

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easySHORT ANSWER3 marks

Given the matrix P = |2 3| |5 7|, calculate its determinant and state the condition for its inverse to exist. (3 marks)

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Part (a) — 2 marks

det(P) = (2)(7) - (3)(5) = 14 - 15 = -1 (1 mk)

det(P) = -1 (1 mk)

Part (b) — 1 mark

The inverse exists if det(P) ≠ 0 (1 mk)

easySHORT ANSWER4 marks

Given matrices A = [[2, 3], [1, 4]] and B = [[5, 6, 7], [8, 9, 10]], identify: (a) whether the product AB is defined. Justify your answer. [2 marks] (b) Calculate the matrix product AB if it is defined. [2 marks]

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Part (a) — 2 marks

The product AB is defined because the number of columns in A (2) equals the number of rows in B (2) (1 mk)

Matrix multiplication is defined when the inner dimensions match (m×n by n×p) (1 mk)

Part (b) — 2 marks

First row of AB: (2*5 + 3*8, 2*6 + 3*9, 2*7 + 3*10) (1 mk)

Second row of AB: (1*5 + 4*8, 1*6 + 4*9, 1*7 + 4*10) (1 mk)

easySHORT ANSWER4 marks

Given matrices A = [[2, 3], [1, 4]] and B = [[5, 6], [7, 8]], calculate: (a) A + B [1 mark] (b) 3A [2 marks] (c) A - B [1 mark]

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Part (a) — 1 mark

A + B = [[2+5, 3+6], [1+7, 4+8]] (1 mk)

Part (b) — 2 marks

3A = 3 * [[2, 3], [1, 4]] (1 mk)

3A = [[6, 9], [3, 12]] (1 mk)

Part (c) — 1 mark

A - B = [[2-5, 3-6], [1-7, 4-8]] (1 mk)

State the determinant of the following 2×2 matrix: |3 4| |2 5|. (2 marks)

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Matrices (addition, multiplication, determinants) — KCSE Mathematics

What You'll Learn

Sample Questions

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