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


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)

Created On
February 19th, 2017
3 years ago
Views
3
Type
 Video
Timeframe
 Pre-class
Perspective
 Introduction
Language
 English
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text/html; charset=utf-8

Suggested classroom activities on matrix inverses.

Created On
February 19th, 2017
3 years ago
Views
2
Type
 Handout
Timeframe
 In-class
Perspective
 Introduction
Language
 English
Content Type
text/html; charset=utf-8

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


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


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

License
GFDL-1.2
Submitted At
September 11th, 2017
 3 years ago
Views
3
Type
 Textbook
Language
 English
Content Type
text/html