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# augment - Using Augmented Matrices to Solve Systems of...

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Augmented Matrices - page 1 Using Augmented Matrices to Solve Systems of Linear Equations 1. Elementary Row Operations To solve the linear system algebraically, these steps could be used. x 5 y z 11 3 z 12 2 x 4 y 2 z8 + - =- = +-= All of the following operations yield a system which is equivalent to the original. (Equivalent systems have the same solution .) Interchange equations 2 and 3 x 5 y z 11 2 x 4 y 2 3 z 12 = Multiply equation 3 by 1 3 x 5 y z 11 2 x 4 y 2 z1 = Multiply equation 2 by 1 2 - x 5 y z 11 x 2 y z4 - - + = Add equation 1 to 2 and replace x 5 y z 11 3 y 15 = equation 2 with the result 1 3 x 5 y z 11 y5 = and add it 5 - xz 14 -= = to equation 1; replace equation 1 with the result Add equation 3 to equation 1; replace x 18 = = equation 1 with the result The solution is (18 , 5 , 4).

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augment - Using Augmented Matrices to Solve Systems of...

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