Quiz9Solutions

Quiz9Solutions - Newberger Math 247 Spring 03 Quiz 4.4 and...

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Unformatted text preview: Newberger Math 247 Spring 03 Quiz 4.4 and 4.7 name: 1. Let A = { a 1 , a 2 , a 3 } and B = { b 1 , b 2 , b 3 } be bases for a vector space V and suppose a 1 = 2 b 1- b 2 + b 3 , a 2 = 3 b 2 + b 3 , and a 3 =- 3 b 1 + b 2 . a. (4 points) Find the change of coordinates matrix from A to B . The columns of the change of coordinate matrix P B←A from A to B are the vectors [ a 1 ] B , [ a 2 ] B , and [ a 3 ] B . The coordinates [ a 1 ] B of a 1 relative to B are the weights when a 1 is written as a linear combination of the vectors in B . Thus since a 1 = 2 b 1- b 2 + b 3 , we have [ a 1 ] B = 2- 1 1 . Similarly, [ a 2 ] B = 3 1 , and [ a 3 ] B = - 3 1 . Thus P B←A = 2 0- 3- 1 3 1 1 1 . b. (4 points) Refereing to the bases A and B above, find [ x ] B where x = a 1- 2 a 2 + 2 a 3 . The coordinates [ x ] A of x relative to A are the weights when x is written as a linear combination of the vectors in A . Thus [ x ] A = 1...
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Quiz9Solutions - Newberger Math 247 Spring 03 Quiz 4.4 and...

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