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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.

Learning Objectives:

  • 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.