diff --git a/College/AU 26/MATH 208 (Matrix Algebra)/Class 10-2.md b/College/AU 26/MATH 208 (Matrix Algebra)/Chapter 1.1 Notes.md similarity index 100% rename from College/AU 26/MATH 208 (Matrix Algebra)/Class 10-2.md rename to College/AU 26/MATH 208 (Matrix Algebra)/Chapter 1.1 Notes.md 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 261a097..66e212e 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 @@ -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 -- \ No newline at end of file + + +$$\begin{bmatrix} +3 & 6 & 2 \\ h & 12 & k +\end{bmatrix} \sim \begin{bmatrix} + +\end{bmatrix}$$ \ No newline at end of file diff --git a/College/AU 26/MATH 208 (Matrix Algebra)/Class 10-5.md b/College/AU 26/MATH 208 (Matrix Algebra)/Class 10-5.md deleted file mode 100644 index ab908ea..0000000 --- a/College/AU 26/MATH 208 (Matrix Algebra)/Class 10-5.md +++ /dev/null @@ -1,3 +0,0 @@ -#uw/notes #uw/class/math208 -- - - -- \ No newline at end of file