MathLab with Mr. Ahmed

MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

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10.4 The Algebra of Matrices

Focus on matrix addition and matrix multiplication dimensions.

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Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Equality, addition and scalar multiplicationWorked steps · five questions02Matrix multiplicationWorked steps · five questions03Writing a system as a matrix equationWorked steps · five questions
Lesson brief and rules

10.4 The Algebra of Matrices

Add matrices entry by entry only when they have matching dimensions.

Worked example 11
01 / Add [3,5][3, 5] and [4,7][4, 7] as row matrices.
02 / Add matching entries.
03 / Answer: [7,12][7, 12]
Worked example 2 · Matrix multiplication dimensions

Can a2×3a 2\times 3 matrix multiply a3×2a 3\times 2 matrix?

Inner dimensions 33 match; outer dimensions give 2×22\times 2. Answer: Yes; result is 2×22\times 2

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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