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Unformatted text preview: Math 20F Quiz 3 (version 1) May 13, 2005 1. (3.2.29) Compute det B 5 , where B = 1 1 1 1 2 1 2 1 . det B = 1 1 1 1 2 1 2 2 = 1 1 1 1 1 2 , by subtracting the first column from the third column of B . Thus, det B = 1 · 1 1 2 = 2. Since the determinant is multiplicative, det B 5 = (det B ) 5 = ( 2) 5 = 32. 2. (4.4.27) Use coordinate vectors to test the linear independence of the set 1 + t 3 , 3 + t 2 t 2 , t + 3 t 2 t 3 of polynomials. Explain your work. The standard basis E for 3 is { 1 , t, t 2 , t 3 } . Hence, 1 + t 3 E = 1 1 , 3 + t 2 t 2 E = 3 1 2 , t + 3 t 2 t 3 E =  1 3 1 The set 1 1 , 3 1 2 ,  1 3 1 is linearly independent since none of the vectors is a linear combination of the other two, as can be seen by observing the location of the zero entries.combination of the other two, as can be seen by observing the location of the zero entries....
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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.
 Spring '03
 BUSS
 Math, Linear Algebra, Algebra

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