- 1.2: Elementary Operations
- We have taken an in depth look at graphical representations of systems of equations, as well as how to find possible solutions graphically. Our attention now turns to working with systems algebraically.
- 1.4: Uniqueness of the Reduced Row-Echelon Form
- As we have seen in earlier sections, we know that every matrix can be brought into reduced row-echelon form by a sequence of elementary row operations. Here we will prove that the resulting matrix is unique; in other words, the resulting matrix in reduced row-echelon does not depend upon the particular sequence of elementary row operations or the order in which they were performed.
Thumbnail: A linear system in three variables determines a collection of planes. The intersection point is the solution. (CC BY-SA 4.0; Fred the Oyster via Wikipedia)