Stitz-Zeager_College_Algebra_e-book

2 a is invertible if and only if ax b has a unique

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Unformatted text preview: nation. Example 8.2.2. Solve the following system using an augmented matrix. Use Gauss-Jordan Elimination to put the augmented matrix into reduced row echelon form. x2 − 3x1 + x4 = 2 2x1 + 4x3 = 5 4x2 − x4 = 3 Solution. We first encode the system into a matrix. (Pay attention to the subscripts!) −3 1 0 12 x2 − 3x1 + x4 = 2 Encode into the matrix 2x1 + 4x3 = 5 − − − − − − − → 2 0 4 0 5 −−−−−−− 4x2 − x4 = 3 0 4 0 −1 3 Next, we get a leading −3 1 2 0 0 4 2 3 1 in the first column of R1. 0 12 1 −1 1 3 Replace R1 with − 3 R1 4 0 5 −−−−−−−→ 2 0 −−−−−−− 0 −1 3 0 4 Carl also finds starting with R3 to be more symmetric, in a purely poetic way. infinite, in fact 0 −1 −2 3 3 4 0 5 0 −1 3 8.2 Systems of Linear Equations: Augmented Matrices 471 Now we eliminate the nonzero entry below our leading 1. 1 1 −3 2 0 0 4 2 1 −1 0 −1 −3 3 3 Replace R2 with −2R1 + R2 2 5 −−−−−−−−− 4 0 −−...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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