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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- Pre-class
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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.

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- June 8th, 2017
- 4 years ago
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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.

- Created On
- August 21st, 2017
- 3 years ago
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- 3
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- Video
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- English
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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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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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- English
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- text/html