1.9soln - Solutions to problems from section 1.9 For...

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Unformatted text preview: Solutions to problems from section 1.9 For questions 2, 4, 10 assume that T is a linear map and find the standard matrix A for T . [Recall that by theorem 10 we know the columns of A will be the images of the e i s under T .] 2. T : R 3 R 2 , T ( e 1 ) = bracketleftbigg 1 3 bracketrightbigg , T ( e 2 ) = bracketleftbigg 4 7 bracketrightbigg , and T ( e 3 ) = bracketleftbigg 5 4 bracketrightbigg where e 1 , e 2 , e 3 are the columns of the 3 3 identity matrix. Solution: A = bracketleftbigg 1 4 5 3 7 4 bracketrightbigg 4. T : R 2 R 2 rotates points (about the origin) through / 4 radians (clockwise). Solution: We must find the images of e 1 = bracketleftbigg 1 bracketrightbigg and e 2 = bracketleftbigg 1 bracketrightbigg under T . Well, lets draw a picture: Thus A = 2 2 2 2 2 2 2 2 10. T : R 2 R 2 first reflects points through the vertical x 2-axis and then rotates points / 2 radians. Solution: Again, lets look at the picture: Thus A = bracketleftbigg 1 1 bracketrightbigg 16. Fill in the missing entries of the matrix assuming that the equation holds for all values of the variables....
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1.9soln - Solutions to problems from section 1.9 For...

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