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# Exam_exam_1_ - MATH 461 Summer I 2006 Exam 1 JUSTIFY ALL...

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MATH 461 – Summer I 2006 – Exam 1 JUSTIFY ALL ANSWERS and SHOW ALL WORK CALCULATORS ARE NOT ALLOWED Put a BOX around your ﬁnal answer to each part. No calculators allowed. You must be careful on arithmetic – check. No proof is needed for TRUE-FALSE questions; just write clearly. A statement is TRUE if it is true without exception. You may assume given matrix equations are well deﬁned (i.e. the matrix sizes are compatible). x 1. (10 pts) Find all solutions for the following system of equations: 11 x 1 + 22 x 2 + 27 x 3 - 16 x 4 = 17 - 3 x 1 - 6 x 2 - 6 x 3 + 9 x 4 = 12 2 x 1 + 4 x 2 + 5 x 3 - 3 x 4 = 3 2. (24 pts) For each of the following, answer TRUE or FALSE. (a) For two n × n matrices A and B , ( AB ) T = A T B T . (b) If U and A are n × n matrices, then the equations UAx = 0 and Ax = 0 have the same solution set. (c) If E is an elementary matrix and b is a vector, then the equations EAx = b and Ax = E - 1 b have the same solution set.

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Exam_exam_1_ - MATH 461 Summer I 2006 Exam 1 JUSTIFY ALL...

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