What Cramer's rule is, and a geometric reason it's true

This rule seems random to many students, but it has a beautiful reason for being true.

A system of linear equations in matrix form can be simplified through the process of Gauss-Jordan elimination to reduced row echelon form. At that point, the solutions can be determined directly from the matrix, without having to...

A system of linear equations represented as an augmented matrix can be simplified through the process of Gaussian elimination to row echelon form. At that point the matrix can be converted back into equations which are simpler and easy...

This program covers the very important topic of Cramer's Rule in matrix algebra. Cramer's Rule is an alternative method used to solve a system of equations. Cramer's Rule is especially useful because it can be applied to a wide range...

Dear linear algebra students, This is what matrices (and matrix manipulation) really look like

This video is about matrix inverses, and in particular, I try to give a bit more intuition for them- rather than just giving you the formula for the determinant, Cramner's rule, the inverse of 2x2 and 3x3 matrices etc. Along the way, we...