M21001-Sp10-t2-sol

# M21001-Sp10-t2-sol - Linear Algebra M21001 - TEST 2 Spring...

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Linear Algebra M21001 - TEST 2 Spring 2010 - Hassan Allouba Your Name (printed, NO signature): You are not allowed to consult with ANYONE but me. You may only use a calculator and your single 8 . 5 × 11 sheet. It is not suﬃcient to just write the answers. You must explain how you arrive at your answers. So, write down ALL the steps. I know you can do it, so relax and enjoy yourself. My best wishes to all of you. 1. (50 points) a) b) 2. (50 points) a) b) c) d) e) TOTAL (100 points) Extra Credit: Write down your name in Egyptian. 1

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Problem 1 Suppose A 3 × 3 is nonsingular (a) (10 points) Write down a linear system Ax = b whose solution is A - 1 * 3 . I.e., what’s b such that x = A - 1 * 3 (the third column in A - 1 )? Solution Ax = e 3 = 0 0 1 (b) (20 points) If A = 2 2 2 1 1 2 1 2 3 , ﬁnd the matrices L , U , and P such that PA = LU ; and explain why P 6 = I 3 × 3 . Solution
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## This note was uploaded on 04/22/2010 for the course MATH 21001 taught by Professor Staff during the Spring '08 term at Kent State.

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M21001-Sp10-t2-sol - Linear Algebra M21001 - TEST 2 Spring...

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