# quiz1sol - general solution is x = 3-s-3 t, y = s, z = 2...

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MAS 4105 Linear Algebra I Solution to Quiz #1 Problem: Find all solutions to the following linear system: x + y + 2 z - u = 1 x + y + z + u = 2 3 x + 3 y + 7 z - 5 u = 2 2 x + 2 y + z + 4 u = 5 Solution: We write the system as an augmented matrix and use Gauss-Jordan elimination. 1 1 2 - 1 . . . 1 1 1 1 1 . . . 2 3 3 7 - 5 . . . 2 2 2 1 4 . . . 5 1 1 2 - 1 . . . 1 0 0 - 1 2 . . . 1 0 0 1 - 2 . . . - 1 0 0 - 3 6 . . . 3 - R 1 + R 2 , - 3 R 1 + R 3 , - 2 R 1 + R 4 1 1 2 - 1 . . . 1 0 0 1 - 2 . . . - 1 0 0 0 0 . . . 0 0 0 0 0 . . . 0 - R 2 + R 3 , - 3 R 2 + R 4 , ( - 1) × R 2 1 1 0 3 . . . 3 0 0 1 - 2 . . . - 1 0 0 0 0 . . . 0 0 0 0 0 . . . 0 - 2 R 2 + R 1 z = 2 u - 1 , x = 3 - y - 3 u. We note that the system is consistent and the matrix above is in reduced row echelon form. Hence the
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Unformatted text preview: general solution is x = 3-s-3 t, y = s, z = 2 t-1 , u = t, where s , t are any real numbers. NOTES. The mean on this quiz was 7.8. Common mistakes were not giving the general solution in parametric form, not specifying s and t . When giving a solution make your answer clear and explain what you are doing. Instead of giving the solutions as above you could provide the solution set { (3-s-3 t,s, 2 t-1 ,t ) : s,t ∈ R } . 1...
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## This note was uploaded on 12/27/2011 for the course MAS 4105 taught by Professor Rudyak during the Spring '09 term at University of Florida.

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