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# 1302 - Fundamentals of Engineering Analysis EGR 1302...

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2/15/2011 1 Fundamentals of Engineering Analysis EGR 1302 Lecture 5, Gaussian Elimination © 2011 Baylor University Slide 1 The Need for a General Solution to Linear Systems 3 x 7 2 3 2 1 = + x x x 2 3 2 3 2 1 = + x x x 5 2 3 2 1 = + x x x the system of equations 2 x Unique Solution, all cross at the same point, the “solution” Det = 0 © 2011 Baylor University Slide 2 1 x We need a method of finding a general solution when the coefficient matrix A is Singular.

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2/15/2011 2 7 3 2 1 2 3 2 1 3 2 1 = + = + + x x x x x x Elementary Row Operations: 7 2 4 3 2 1 = + x x x We will use three elementary row operations to solve this set of linear equations by Gaussian Elimination. © 2011 Baylor University Slide 3 2. Swap two rows - Using Elementary Row Operations to Solve by Gaussian Elimination 7 3 2 1 2 3 2 1 3 2 1 = + = + + x x x x x x 5 7 0 1 2 3 2 3 2 1 = + + = + + x x x x x Step 1: Use Rule 3 to eliminate from rows 2 & 3: 1 x 1. Keep Row 1 the same 1 2 ' 2 * 2 r r r + = 2.
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1302 - Fundamentals of Engineering Analysis EGR 1302...

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