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College/AU 26/MATH 208 (Matrix Algebra)/Chapter 1.2 Notes.md

@@ -13,4 +13,10 @@
 	\end{bmatrix} \end{gathered}$$
 	- Same elementary operations can be used with augmented matrices, now it is with rows instead of equations.
 - gaussian elimination
-	- this is converting a matrix to **echelon form** (or row echel)
+	- this is converting a matrix to **echelon form** (or row echelon form)
+		- this is when every leading term is a column to the left of the one below it and any zero rows are at the bottom
+	- once the augmented matrix is in echelon form it can be converted back into a linear system of equations (that is not in echelon form) and solved
+	- the pivot is the coefficient of the leading terms (or the fr)
+- Gauss-Jordan elimination
+	- this can make it easier to find the general solution of the system
+	- 1. multiply each nonzero row by the inverse of the pivot so every pivot is 1