Linear Systems and Matrix FormalismAdam GamzonThis handout will examine row-reduction and Gauss-Jordan elimination in more detail witha heavy emphasis on examples. In class, we introduced matrices as a way of encoding all ofthe information in a given linear system in order to save on the bookkeeping necessary whileperforming the algorithm for Gauss-Jordan elimination. To recall how this goes, let’s look at anexample.Example 1.Consider the system2x1+4x2+3x3+5x4=34x1+8x2+7x3x4=4-2x1-4x2x3x4=0x1+2x2x3-x4=2.Thecoefcient matrixfor this system is0BB@24354875-2-43 4122-11CCA.As mentioned in class, the coefcient matrix will be less important for us early in the coursebut it will come in handy in a couple of chapters.Theaugmented matrixfor this system isA=
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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).