Quiz 1 Solution - MATH 2120 Quiz#1 SOLUTIONS\/5 Problem 1 Use Gauss-Jordan elimination to solve the following system of linear equations x 3y z = 7 3x 9y

Quiz 1 Solution - MATH 2120 Quiz#1 SOLUTIONS/5 Problem 1...

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MATH 2120: Quiz #1 – SOLUTIONS / 5 Problem 1: Use Gauss-Jordan elimination to solve the following system of linear equations. x + 3 y + z = 7 3 x + 9 y + 7 z = 6 bracketleftbigg 1 3 1 7 3 9 7 6 bracketrightbigg R 2 - 3 R 1 −−−−−→ bracketleftbigg 1 3 1 7 0 0 4 15 bracketrightbigg R 2 / 4 −−−−→ R 1 - R 2 bracketleftbigg 1 3 0 43 4 0 0 1 15 4 bracketrightbigg = x = 43 4 3 y y is free z = 15 4 = x = 43 4 3 t y = t (where t R is arbitrary) z = 15 4 / 5 Problem 2: Consider the following linear system, in which k is a constant. x + ky = 1 kx + y = 1 For what value(s) of k (if any) will the system have:

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