# The inverse of a matrix (if it exists) can be found by row reducing the matrix augmented by the identity matrix.

math.la.t.mat.inv.augmented

# Finding the inverse of a matrix and using it to solve a linear system

Matrix inverses are motivated as a way to solve a linear system. The general algorithm of finding an inverse by row reducing an augmented matrix is described, and then implemented for a 3x3 matrix. Useful facts about inverses are stated and then illustrated with sample 2x2 matrices. (put first: need Example of finding the inverse of a 3-by-3 matrix by row reducing the augmented matrix)

##### math.la.t.eqn.mat.inv
Created On
February 19th, 2017
6 years ago
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3
Type
Video
Timeframe
Pre-class
Perspective
Introduction
Language
English
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# Inverse of a Matrix: In-Class Activities

Suggested classroom activities on matrix inverses.

##### math.la.t.mat.inv.augmented
Created On
February 19th, 2017
6 years ago
Views
2
Type
Handout
Timeframe
In-class
Perspective
Introduction
Language
English
Content Type
text/html; charset=utf-8

# Invertible Matrix Theorem

Statements that are equivalent to a square matrix being invertible; examples.

##### math.la.d.mat.inv
Created On
August 21st, 2017
5 years ago
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3
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Video
Language
English
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text/html; charset=utf-8

# Matrix inverses

Properties of matrix inversion: inverse of the inverse, inverse of the transpose, inverse of a product; elementary matrices and corresponding row operations; a matrix is invertible if and only if it is row-equivalent to the identity matrix; row-reduction algorithm for computing matrix inverse

##### math.la.t.equiv.identity
Created On
August 25th, 2017
5 years ago
Views
3
Type
Video
Language
English
Content Type
text/html; charset=utf-8

# Matrix Inverses and Systems of Linear Equations - A First Course in Linear Algebra

The inverse of a square matrix, and solutions to linear systems with square coefficient matrices, are intimately connected.