Spring 2003 - Buss' Class - Quiz 2.5

# Spring 2003 - Buss' Class - Quiz 2.5 - Name Student ID...

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Name: Thursday section time: Student ID: Math 20F - Linear Algebra - Spring 2003 Self-Assessment Quiz #2.5 — April 25 1. Find the determinant of the following matrix: 1212 2422 2364 - 1022 . ANSWER: - = 12 00 0 - 2 0 - 14 0 02 34 =( - 1) 0 - 0 0 - 2 - 1) 0 - 0 0 - 2 - 1)( - 1) 0 - 14 0 0 0 11 4 0 - 2 =2 2 . 2. Let v - 3 , 3 , 1 , 1) T , u 1 =(1 , 4 , 3 , 2) T , u 2 , - 2 , - 1 , 0) T , and u 3 , 1 , 1 , 1 , ) T .I s v Span ( u 1 , u 2 , u 3 )? Prove your answer. If “Yes”, express v a linear combination of u 1 , u 2 , and u 3 . ANSWER: Solve the equation A x = v , where A u 1 u 2 u 3 ) : ˆ 11 1 - 3 4 - 21 3 3 - 1 20 1 1 ! ˆ 111 - 3 0 - 6 - 3 15 0 - 4 - 2 10 0 - 2 - 1 7 ! ˆ - 3 0 - 6 - 3 15 0 - 4 - 2 10 000 2 ! . (The last step subtracts 1 2 times the third from the fourth row.) Then, there is no solution to A x = v ,so v / Span ( u 1 , u 2 , u 3 ) . BONUS ANSWER: I meant to ask the question with the vector w - 3 , 3 , 1 , - 1) T instead of v . In this case the answer is obtained
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## This note was uploaded on 04/23/2008 for the course MATH 20F taught by Professor Buss during the Spring '03 term at UCSD.

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