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

math.la.t.eqn.mat.inv

# 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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# Lagrange Interpolation - Ximera

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.

##### math.la.d.lintrans.arb
Created On
June 8th, 2017
5 years ago
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# 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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# Matrix Inverses, definition and 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.

##### math.la.t.eqn.mat.inv
Created On
August 22nd, 2017
5 years ago
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4
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Video
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English
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# Matrix Inverses and Nonsingular Matrices - A First Course in Linear Algebra

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.