Midterm_01_Spring_Quarter_2010-02-01

Midterm_01_Spring_Quarter_2010-02-01 - 22A Section 01...

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22A - Section 01 Midterm 1 - February 1, 2010 Name Version 2 Use of texts, notes or calculators is not allowed. TRY THIS TEST TAKING STRATEGY Here is a good test taking strategy. Do the easy problems first! Read over the entire test doing only those problems whose solution is immediately apparent to you. Then make a second pass at the test trying to solve the easiest of the remaining problems. Continue in this way until you are done. Good luck! Problem Points Score 1 10 2 05 3 10 4 20 5 10 6 10 7 05 8 10 9 10 10 10 Total 100 Extra Credit 10 0
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22A - Section 01 Midterm 1 - February 1, 2010 Name 1. (10 points total) Let A be an n × n matrix and suppose that A is nonsingular . (a) (2.5 points) What – if anything – can you say about the determinant of the matrix A , det ( A )? Justify your answer. (b) (2.5 points) What – if anything – can you say about solutions of the matrix equation A x = 0 ? Justify your answer. (c) (2.5 points) What – if anything – can you say about solutions of the matrix equation A x = b where b is an arbitrary nonzero n -vector? Justify your answer. (d) (2.5 points) Let B be any n × n matrix and consider that the matrix C = AB . What – if anything – can you say about solutions of the matrix equation C x = 0 . Justify your answer. 1
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22A - Section 01 Midterm 1 - February 1, 2010 Name 2. (5 points) Let V be a vector space and let W V be a subset of V . What do you need to show in order to demonstrate that W is a vector space in its own right; i.e., that W is a subspace of V ?
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