You can "invert" matrices to solve equations...sometimes!

With numbers, we can solve equations like 3x=7 by multiplying both sides by 1/3. Wonderfully, there is an analogue for matrix equations Ax=b called the inverse of A, and if you have it, you can solve systems of equations really easily! Unfortunately, just like how 0 doesn't have an inverse in numbers, a lot of matrices don't have inverses either.

Learning Objectives:
1) Define the inverse of a matrix
2) Algebraically show how if you know the inverse, you can solve any Ax=b, and solve it uniquely!

This video is part of a Linear Algebra course taught at the University of Cincinnati.

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