diff --git a/College/AU 26/MATH 208 (Matrix Algebra)/Chapter 1.2 Notes.md b/College/AU 26/MATH 208 (Matrix Algebra)/Chapter 1.2 Notes.md index 1c92df9..ac54f76 100644 --- a/College/AU 26/MATH 208 (Matrix Algebra)/Chapter 1.2 Notes.md +++ b/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 - - matricies with all constant terms of a linear system of equations are called a **augmented matrix** - - $$\begin{align*} a_{11}x_{1} + a_{12}x_{2} + a_{13} \end{align*}$$ \ No newline at end of file +- matrices can be used to simplify when working with systems of linear equations + - matrices with all constant terms of a linear system of equations are called a **augmented matrix** + - $$\begin{gathered} \text{Linear System} \\ a_{11}x_{1} + a_{12}x_{2} + a_{13}x_{3} = b_{1} \\ a_{21}x_{1} + a_{22}x_{2} + a_{23}x_{3} = b_{2} \\ a_{31}x_{1} + a_{32}x_{2} + a_{33}x_{3} = b_{3} \end{gathered} \quad \sim \quad \begin{gathered} \text{Augmented Matrix} \\ \begin{bmatrix} + a_{11} & a_{12} & a_{13} & b_{1} \\ a_{21} & a_{22} & a_{23} & b_{2} \\ a_{31} & a_{32} & a_{33} & b_{3} + \end{bmatrix} \end{gathered}$$ + - 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) \ No newline at end of file