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College/AU 26/MATH 208 (Matrix Algebra)/Chapter 1.2 Notes.md
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- this is converting a matrix to **echelon form** (or row echelon form) - 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 - 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 - 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) - the pivot is the coefficient of the leading terms (or the free variables)
- Gauss-Jordan elimination - Gauss-Jordan elimination
- this can make it easier to find the general solution of the system - 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 - 1. multiply each nonzero row by the inverse of the pivot so every pivot is 1