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

@@ -15,8 +15,10 @@
 - Gaussian Elimination
 	- 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
+	- Very important method for many applications, used to solve systems of linear equations
 	- 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 free variables)
+		- The first non-zero term in a row
 - 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
@@ -27,4 +29,10 @@
 	- when the $b_{n}$ term of each equation is zero
 	- There is a "trivial solution" where each variable equals zero
 	- There can also be non-trivial solutions 
-- 
+
+
+$$\begin{bmatrix}
+3 & 6 & 2 \\ h & 12 & k
+\end{bmatrix} \sim \begin{bmatrix}
+
+\end{bmatrix}$$