Chapter 8.4 - Systems of Linear Equations - Matrix Inverses
Khan Academy - Inverse of 3-by-3 Matrix
Khan Academy - Inverse of a 2-by-2 Matrix
Khan Academy - Matrix Inverse Part 1
Systems of Linear Equations - Matrix Inverse
TMM 002 PRECALCULUS (Revised March 21, 2017)
3. Equations and Inequalities:
3a. Recognize function families as they appear in equations and inequalities and choose an appropriate solution methodology for a particular equation or inequality, as well as communicate reasons for that choice.*
Inverse of a Matrix
Recall that a simple linear equation of the form ax = b has the solution x = b/a = a-1.b, a ≠ 0.
As noted in earlier modules, a system of linear equations can be written as AX = B, where A and B are known matrices and X is the variable matrix. Note that this equation resembles a simple linear equation. The question is does the solution look like X = A-1. B? If so, what is A-1 and how to find it?
In this module we will learn about matrix inverse and use the same, if it exists, to find the solution to a system of linear equations.
Review: Augmented matrices and Gauss-Jordan Elimination method.
- Square matrix, singular and non-singular matrices
- Identify matrix
- Inverse of a non-singular matrix
- Use the inverse, when it exists, to find the solution to a system of linear equations.