hw7 - Math 152, Spring 2010 Assignment #7 Notes: Each...

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Math 152, Spring 2010 Assignment #7 Notes: Each question is worth 5 marks. Due in class: Monday, March 8 for MWF sections; Tuesday, March 9 for TTh sections. Solutions will be posted Tuesday, March 9 in the afternoon. No late assignments will be accepted. 1. Let T and S denote the linear transformations of R 2 which reflect vectors in the x -axis, and rotate vectors by 30 degrees clockwise. (a) Find matrices representing S and T . (b) Find matrices representing ST and TS . 2. Suppose T is a linear transformation from R 2 to R 3 , given by the matrix 1 1 1 0 0 2 . If L is a line in R 2 , passing through the point (1 , 1) and in the direction of the vector ~v = (1 , 2 , 1), then find the image of the line L under T . (Note: the vectors in this problem and the problem below have been written as row vectors to save space.) 3. Suppose T is a linear transformation from R 3 to R 3 such that T ( e 1 ) = (1 , 1 , 1), T ( e 2 ) = (1 , 2 , 1), and T ( e 3 ) = (1 , 0 , 1).
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hw7 - Math 152, Spring 2010 Assignment #7 Notes: Each...

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