Spring 2005 - Nagy's Class - Quiz 3

Spring 2005 - Nagy's Class - Quiz 3 - Math 20F Quiz 3...

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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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Spring 2005 - Nagy's Class - Quiz 3 - Math 20F Quiz 3...

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