The inverse of a matrix can be used to solve a linear system.

math.la.t.eqn.mat.inv


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
4 years ago
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 Video
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 Pre-class
Perspective
 Introduction
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 English
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This is a guided discovery of the formula for Lagrange Interpolation, which lets you find the formula for a polynomial which passes through a given set of points.

Created On
June 8th, 2017
3 years ago
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2
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 Handout
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 Application
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 English
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Statements that are equivalent to a square matrix being invertible; examples.


Definition of the inverse of a matrix, examples, uniqueness; formula for the inverse of a 2x2 matrix; determinant of a 2x2 matrix; using the inverse to solve a system of linear equations.

Created On
August 22nd, 2017
3 years ago
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3
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 Video
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 English
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text/html; charset=utf-8

We saw in Theorem CINM that if a square matrix \(A\) is nonsingular, then there is a matrix \(B\) so that \(AB=I_n\text{.}\) In other words, \(B\) is halfway to being an inverse of \(A\text{.}\) We will see in this section that \(B\) automatically fulfills the second condition (\(BA=I_n\)). Example MWIAA showed us that the coefficient matrix from Archetype A had no inverse. Not coincidentally, this coefficient matrix is singular. We will make all these connections precise now. Not many examples or definitions in this section, just theorems.

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GFDL-1.2
Submitted At
September 11th, 2017
 3 years ago
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3
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 Textbook
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 English
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text/html