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College/AU 26/MATH 208 (Matrix Algebra)/Chapter 1.2 Notes.md
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- 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
- 2. manipulate so every pivot only has zeros above it - 2. manipulate so every pivot only has zeros above it
- This means that leading variables are only in the equations that they lead - This means that leading variables are only in the equations that they lead
- This puts the matrix in reduced echelon form - This puts the matrix in **reduced echelon form**
- Homogeneous linear system - Homogeneous linear system
- when the $b_{n}$ term of each equation is zero - when the $b_{n}$ term of each equation is zero
- There is a "trivial solution" where each variable equals zero - There is a "trivial solution" where each variable equals zero
- There can also be non-trivial solutions - There can also be non-trivial solutions
- -