q1f08solnm05

q1f08solnm05 - x 1 , x 2 , x 3 , x 4 ) = . . . . x 1-2 x 2...

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MATH 205 Quiz 1 Soln September, 2008 NAME: 1. Find the reduced row echelon form of the augmented matrix of the following system of equations. x 1 + x 2 + x 3 - 2 x 4 - x 5 = 2 - x 1 - x 2 - 2 x 3 + x 4 - x 5 = 2 Do NOT solve ! 2 x 1 + 2 x 2 - 3 x 4 = 0 Solution: ( A | ± b ) 1 1 1 - 2 - 1 | 2 0 0 - 1 - 1 - 2 | 4 0 0 - 2 1 2 | - 4 1 1 0 - 3 - 3 | 6 0 0 1 1 2 | - 4 0 0 0 3 6 | - 12 1 1 0 0 3 | - 6 0 0 1 0 0 | 0 0 0 0 1 2 | - 4 2. The following consistent system of equations is already reduced. Identify the free variables, find the solution, and write the solution in the form (
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Unformatted text preview: x 1 , x 2 , x 3 , x 4 ) = . . . . x 1-2 x 2 + 3 x 4 = 2 x 3-x 4 =-1 free variables: x 2 = a, x 4 = b. use of equations: x 1 = 2 + 2 x 2-3 x 4 = 2 + 2 a-3 b, x 3 =-1 + x 4 =-1 + b, vector form (in R 4 ): ( x 1 , x 2 , x 3 , x 4 ) = (2 + 2 a-3 b, a,-1 + b, b )....
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