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Inverting matrices

12 videos
4 skills
Multiplying by the inverse of a matrix is the closest thing we have to matrix division. Like multiplying a regular number by its reciprocal to get 1, multiplying a matrix by its inverse gives us the identity matrix (1 could be thought of as the "identity scalar"). This tutorial will walk you through this sometimes involved process which will become bizarrely fun once you get the hang of it.

Finding the determinant of a 2x2 matrix

VIDEO 1:10 minutes
Hint for finding the determinant of a 2x2 matrix

Determinant of a 2x2 matrix

PRACTICE PROBLEMS
Find the determinant of a 2x2 matrix

Inverse of a 2x2 matrix

VIDEO 2:48 minutes
Example of calculating the inverse of a 2x2 matrix

Idea behind inverting a 2x2 matrix

VIDEO 14:14 minutes
What the inverse of a matrix is. Examples of inverting a 2x2 matrix.

Inverse of a 2x2 matrix

PRACTICE PROBLEMS
Find the inverse of a 2x2 matrix

Matrices to solve a system of equations

VIDEO 16:33 minutes
Using the inverse of a matrix to solve a system of equations.

Matrices to solve a vector combination problem

VIDEO 14:20 minutes
Using matrices to figure out if some combination of 2 vectors can create a 3rd vector

Determinant of a 3x3 matrix

PRACTICE PROBLEMS
Find the determinant of a 3x3 matrix

Inverting 3x3 part 1: Calculating matrix of minors and cofactor matrix

VIDEO 8:47 minutes
Beginning our quest to invert a 3x3 matrix. We calculate the matrix of minors and the cofactor matrix.

Inverting 3x3 part 2: Determinant and adjugate of a matrix

VIDEO 6:23 minutes
Finishing up our 3x3 matrix inversion

Classic video on inverting a 3x3 matrix part 1

VIDEO 16:44 minutes
Inverting a 3x3 matrix

Classic video on inverting a 3x3 matrix part 2

VIDEO 13:36 minutes
Using Gauss-Jordan elimination to invert a 3x3 matrix.

Singular matrices

VIDEO 14:27 minutes
When and why you can't invert a matrix.

Inverse of a 3x3 matrix

PRACTICE PROBLEMS
Find the inverse of a 3x3 matrix