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Unformatted text preview: A ). c. Does there exist a vector ~x R 2 such that T ( ~x ) = 12 4 3 ? Explain. Problem 2. Consider a line L in the coordinate plane, running through the origin. The reection about L is a linear transformation in the form ref L ( ~x ) = a b ba ~x where a 2 + b 2 = 1. What is the composition ref L ref L ? Give a geometric interpretation. Problem 3. Consider a line L in the form y = mx . a. Find a unit vector ~u which is parallel to L . (Express its entries in terms of m .) b. Find the matrix of the projection proj L ( ~x ) of ~x onto L . (Express its entries in terms of m .) 1...
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 Spring '08
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 Linear Algebra, Algebra

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