quiz - MATH 407 QUIZ NAME(Please print Solutions There are...

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MATH 407 QUIZ NAME (Please print): Solutions There are 2 problems. Stop now and make sure you have both problems. If you do not have them both, then request a new quiz. The first problem is worth 30 points and the second is worth 45 points for a total of 75 points. Show all of your work and follow the directions provided. Partial credit will be given for partial solutions. CALCULATORS ARE NOT ALLOWED! Problem Score 1 2 Total

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Page 2 of 2 1. [a](15 points) Under what conditions is the set S IR n a subspace of IR
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Unformatted text preview: [b](15 points) Let A be a linear transformation from IR n to IR m with m < n . Give the deﬁnition for the null space of A and provide a simple lower bound for its dimension. 2. Consider the system-x 1 + 4 x 3 = 200-x 1 + x 2 + 9 x 3 = 200 2 x 1-x 2 + 7 x 3 = 200 . (a)(15 points) Write the augmented matrix corresponding to this system. (b)(20 points) Reduce the augmented system in part (a) to echelon form. (c)(10 points) Describe the set of solutions to the given system....
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