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Math 54 - Quiz 01 Ans, Spring 2006 (2)

# Math 54 - Quiz 01 Ans, Spring 2006 (2) - x y z = 5 2 x-y z...

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Math 54, Quiz 1 Solutions Sections 202/203 GSI Carter 1. For each of the following statements, write the word “true” or “false.” (a) xy = k is a linear equation, where x and y are variables and k is a constant. False, because the variables are being multiplied together. (b) The following system of equations has at least one solution. x + y - z = 0 3 x + 2 y + z = 0 x - 2 y - 2 x = 0 7 x - y + 8 z = 0 True, because every homogeneous system has at least the trivial solution. 2. Find all solutions to the following system of equations.
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Unformatted text preview: x + y + z = 5 2 x-y + z = 10 4 x + y + 3 z = 20 The augmented matrix associated to this system can be row reduced as follows:   1 1 1 5 2-1 1 10 4 1 3 20     1 1 1 5-3-1-3-1     1 1 1 5 1 1 3   Therefore the choice of z is arbitrary, and we have that y =-z 3 and x = 5-y-z = 5-2 z 3 . 1...
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