Quiz 1 - Solutions

# Quiz 1 - Solutions - equation A x = b meaning b is not in...

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Math 54 Quiz 1 Mike Hartglass September 4, 2010 1.) (3 points) Solve the following system of equations x 1 - 3 x 3 = 8 2 x 1 + 2 x 2 + 9 x 3 = 7 x 2 + 5 x 3 = - 2 The corresponding augmented matrix is: 1 0 - 3 8 2 2 9 7 0 1 5 - 2 1 0 - 3 8 0 2 15 - 9 0 1 5 - 2 1 0 - 3 8 0 1 5 - 2 0 2 15 - 9 1 0 - 3 8 0 1 5 - 2 0 0 5 - 5 1 0 - 3 8 0 1 0 3 0 0 1 - 1 1 0 0 5 0 1 0 3 0 0 1 - 1 meaning x 1 = 5, x 2 = 3 and x 3 = - 1. 1

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2.) Let A = 1 4 - 2 - 1 1 3 0 5 1 and b = 0 0 1 . Is b in the span of the columns of A ? Explain. b is in the span of the columns of A if and only if A x = b has a solution. The corresponding augmented matrix for this system is: 1 4 - 2 0 - 1 1 3 0 0 5 1 1 1 4 - 2 0 0 5 1 0 0 5 1 1 1 4 - 2 0 0 5 1 0 0 0 0 1 . The last matrix is that of an inconsistent system, so there is no solution to the
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Unformatted text preview: equation A x = b meaning b is not in the span of the columns of A . 3.) The following augmented matrices represent systems of equations. For each case determine if there is one solution, inﬁnitely many solutions or no solution. ± 1 0 2 0 0 4 ² No solutions 1 5 3 8 0 1 4 5 0 0 1 9 0 0 0 0 One solution 1 4 6 10 0 3 4 1 0 0 2 5 One solution ± 1 0 3 0 0 0 ² Inﬁnitely many solutions 2...
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