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# Exam_exam_1(3) - MATH 461-01 Spring 2006 Exam 1 JUSTIFY ALL ANSWERS and SHOW ALL WORK CALCULATORS ARE NOT ALLOWED Answer each question on a

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MATH 461-01** – Spring 2006 – Exam 1 JUSTIFY ALL ANSWERS and SHOW ALL WORK CALCULATORS ARE NOT ALLOWED Answer each question on a separate sheet of paper. Use the back side if necessary. On each sheet, put your name, your section leader’s name and your section meeting time. 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. You may assume given matrix equations are well deﬁned (i.e. the matrix sizes are compatible). 1. (15 pts) Find all solutions for the following system of equations: x 1 + 2 x 2 + 2 x 3 - x 4 = 2 - x 1 - 2 x 2 - 2 x 3 + 3 x 4 = 4 2 x 1 + 4 x 2 + 5 x 3 - 3 x 4 = 3 2. (a) (18 pts) For each of the following, answer TRUE or FALSE. i. A 3 × 4 matrix has 3 columns. ii. If U is an invertible matrix, then the equations UAx = 0 and Ax = 0 have the same solution set.

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## This note was uploaded on 04/05/2008 for the course MATH 493 taught by Professor Jake during the Spring '08 term at Maryland.

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Exam_exam_1(3) - MATH 461-01 Spring 2006 Exam 1 JUSTIFY ALL ANSWERS and SHOW ALL WORK CALCULATORS ARE NOT ALLOWED Answer each question on a

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