Linear_Algebra_03

# Linear_Algebra_03 - Solving Systems of Linear Equations by...

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Solving Systems of Linear Equations by the Gaussian Elimination and Gauss-Jordan Elimination Methods J. Vanualailai * April 26, 2013 * School of Computing, Information & Mathematical Sciences, University of the South Pacific, Suva, Fiji.

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Systems of Linear Equations In general, a system of linear equations has m equations and n variables denoted by x 1 ,x 2 , · · · ,x n . a 11 x 1 + a 12 x 2 + a 13 x 3 + · · · + a 1 n x n = b 1 a 21 x 1 + a 22 x 2 + a 23 x 3 + · · · + a 2 n x n = b 2 a 31 x 1 + a 23 x 2 + a 33 x 3 + · · · + a 3 n x n = b 3 . . . . . . . . . . . . . . . . . . a m 1 x 1 + a m 2 x 2 + a m 3 x 3 + · · · + a mn x n = b m In matrix form, this is A x = b where A = a 11 a 12 a 13 · · · a 1 n a 21 a 22 a 23 · · · a 2 n a 31 a 23 a 33 · · · a 3 n . . . . . . . . . . . . . . . a m 1 a m 2 a m 3 · · · a mn , x = x 1 x 2 x 3 . . . x n , b = b 1 b 2 b 3 . . . b m
Augmented Matrix We will study two methods that uses matrices to solve our system of

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