matrix formalism-page1

matrix formalism-page1 - Linear Systems and Matrix...

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Linear Systems and Matrix Formalism Adam Gamzon This handout will examine row-reduction and Gauss-Jordan elimination in more detail with a heavy emphasis on examples. In class, we introduced matrices as a way of encoding all of the information in a given linear system in order to save on the bookkeeping necessary while performing the algorithm for Gauss-Jordan elimination. To recall how this goes, let’s look at an example. Example 1. Consider the system 2 x 1 +4 x 2 +3 x 3 +5 x 4 =3 4 x 1 +8 x 2 +7 x 3 x 4 =4 - 2 x 1 - 4 x 2 x 3 x 4 =0 x 1 +2 x 2 x 3 - x 4 =2 . The coe f cient matrix for this system is 0 B B @ 24 3 5 48 7 5 - 2 - 43 4 12 2 - 1 1 C C A . As mentioned in class, the coe f cient matrix will be less important for us early in the course but it will come in handy in a couple of chapters. The augmented matrix for this system is A =
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This note was uploaded on 11/22/2011 for the course MATH 255 taught by Professor Staff during the Spring '10 term at UMass (Amherst).

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