math 235 hw4 - Homework 4, Due March 9 Adam Gamzon Related...

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Unformatted text preview: Homework 4, Due March 9 Adam Gamzon Related reading: sections 3.3 and 3.4 from the text and the handout on dimension 1. Let T : R 3 R 3 be the linear transformation given by the matrix 5- 4- 2- 4 5- 2- 2- 2 8 . Let B = 2 2 1 , 1- 1 , 1- 2 . This is a basis of R 3 . (a) Compute the matrix [ T ] BB . Solution: We have 5- 4- 2- 4 5- 2- 2- 2 8 2 2 1 = , 5- 4- 2- 4 5- 2- 2- 2 8 1- 1 = 9- 9 , 5- 4- 2- 4 5- 2- 2- 2 8 1- 2 = 9- 18 , so the coordinate vector of each of these with respect to B is , 9 , 9 respectively. Hence [ T ] BB = 0 0 0 0 9 0 0 0 9 . (b) If x = 1 1 1 , find [ x ] B ....
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math 235 hw4 - Homework 4, Due March 9 Adam Gamzon Related...

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