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Berkeley MATH 54 - Quiz 1

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Name:Section: 9:00-10:00 11:00-12:00Math 54 Quiz 1 SOLUTIONSJanuary 28, 2008GSI: Rob BayerYou have twenty minutes to complete this quiz. You must show your work in order toreceive partial credit.1. (3 pts) Find the solution to the system of equationsx1+ − 3x3= 82x1+ 2x2+ 9x3= 7x2+ 5x3= −2Augmented Matrix:1 0 −3 82 2 9 70 1 5 −2r2= r2− 2r1:1 0 −3 80 2 15 −90 1 5 −2r2= r2− 2r3:1 0 −3 80 0 5 −150 1 5 −2r2: −5x3= 5, so x3= −1r3: x2+ 5(−1) = −2, so x2= −2 + 5 = 3r1: x1− 3(−1) = 8, so x1= 5The solution is thus (5, 3, −1)2. (3 pts) Find the reduced echelon form of3 6 0 96 12 2 26−1 −2 −1 −413r1,12r2:1 2 0 33 6 1 13−1 −2 −1 −4r2= r2− 3r1, r3= r3− r1:1 2 0 30 0 1 40 0 1 1r3= r3− r2:1 2 0 30 0 1 40 0 0 −3−13r3:1 2 0 30 0 1 40 0 0 1r2= r2− 4r3, r1= r1− 3r31 2 0 00 0 1 00 0 0 13. (4 pts) The matrices below represent systems of linear equations. For each matrix,determine how many solutions (if any) the corresponding system of equations has.(a)1 3 8 −60 2 −2 10 0 −7 0: one (b)4 −1 8 90 −1 −2 10 0 3 60 0 0 0: one(c) 1 0 00 0 1!: none (d) 1 0 00 0 0!: infinitely


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Berkeley MATH 54 - Quiz 1

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