Midterm_01_Spring_Quarter_2009-05-04

# Midterm_01_Spring_Quarter_2009-05-04 - 22A - Section 01...

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22A - Section 01 Midterm 1 - May 4, 2009 Name 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 15 4 20 5 10 6 10 7 05 8 05 9 10 10 10 Total 100 Extra Credit 10 0

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Midterm 1 - May 4, 2009 Name 1. (10 points total) Let A and B both be n × n matrices and suppose that the matrix A is nonsingular and the matrix B is singular . (a) (2.5 points) What - if anything - can you say about whether the matrix AB is singular or not? Justify your answer. (b) (2.5 points) What can you say about solutions of the matrix equation A x = 0 ? Justify your answer. (c) (2.5 points) What can you say about solutions of the matrix equation B x = 0 ? Justify your answer. (d) (2.5 points) What can you say about solutions of the matrix equation B x = b where b is an arbitrary nonzero n -vector? Justify your answer. 1
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## This note was uploaded on 05/14/2010 for the course MATH 22a taught by Professor Chuchel during the Winter '08 term at UC Davis.

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Midterm_01_Spring_Quarter_2009-05-04 - 22A - Section 01...

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