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

@@ -6,6 +6,11 @@
 	- Multiply an equation by a nonzero constant
 	- Add a multiple of one equation to another
 	- $\sim$ is used to indicate the transformation between equivalent linear systems
-- matricies can be used to simplify when working with systems of linear equations
+- matrices can be used to simplify when working with systems of linear equations
-	- matricies with all constant terms of a linear system of equations are called a **augmented matrix**
+	- matrices with all constant terms of a linear system of equations are called a **augmented matrix**
-	- $$\begin{align*} a_{11}x_{1} + a_{12}x_{2} + a_{13}  \end{align*}$$
+	- $$\begin{gathered} \text{Linear System} \\ a_{11}x_{1} + a_{12}x_{2} + a_{13}x_{3} = b_{1} \\ a_{21}x_{1} + a_{22}x_{2} + a_{23}x_{3} = b_{2} \\ a_{31}x_{1} + a_{32}x_{2} + a_{33}x_{3} = b_{3} \end{gathered} \quad \sim \quad \begin{gathered} \text{Augmented Matrix} \\ \begin{bmatrix}
+	a_{11} & a_{12} & a_{13} & b_{1} \\ a_{21} & a_{22} & a_{23} & b_{2} \\ a_{31} & a_{32} & a_{33} & b_{3} 
+	\end{bmatrix} \end{gathered}$$
+	- 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)