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.

MathLabwith Mr. Ahmed
Free preview

10.5 Inverses of Matrices and Matrix Equations

Focus on invertibility and solve a matrix equation.

Before you solve

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.

01Inverse of a 2 × 2 matrixWorked steps · five questions02Solving systems with inverse matricesWorked steps · five questions
Lesson brief and rules

10.5 Inverses of Matrices and Matrix Equations

For A=[abcd],det⁡A=ad−bcA=\begin{bmatrix}a & b \\ c & d\end{bmatrix}, \det A=ad-bc; invert only if det⁡A≠0\det A\ne 0.

Worked example 11
01 / Is [3004]\begin{bmatrix}3 & 0 \\ 0 & 4\end{bmatrix} invertible?
02 / Determinant 3⋅4=12≠03\cdot 4=12\ne 0, so an inverse exists.
03 / Answer: Yes
Worked example 2 · Solve a matrix equation

If AA is invertible and AX=BAX=B, what equals XX?

Left multiply both sides by A−1A^{-1}. Answer: A−1BA^{-1}B

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.

Read this lesson preview