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Lecture

# Gaussian Elimination

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School
Department
Mathematics
Course
MATH 2331
Professor
Rita Jimenez Rolland
Semester
Spring

Description
Linear Algebra Notes Gaussian Elimination February 2, 2014 Example. Find the solution(s) of the system of equations. 0 . 1 0 1 1 ▯1 0 0 4 . 2 x1▯ x2+ 4x 5 = 2 B C x1 = 2 + x2▯ 4x5 @ x3▯ x5 = 2A ! B . C ! x3 = 2 + x5 @ 0 0 1 0 ▯1 . 2A x4▯ x5 = 3 . x4 = 3 + x5 0 0 0 1 ▯1 . 3 In the above example, x and x are known as free variables. 2 5 Free variables ) 1 solutions. Take free variable2 x = t 2 R an5 x = s 2 R. x = 2 + t ▯ 4s x = t x = 2 + s x = s + 2 x = s (also write in vector notation) 1 2 3 4 5 Systems with solutions are consistent. Those without solutions are inconsistent. Requirements: ▯ leading coe▯cients in each equation equal to 1 ▯ leading variable in each equation doesn’t appear elsewhere ▯ leading variables appear in a "natural order" 2x + 4x ▯ 2x + 2x + 4x
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