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Unformatted text preview: Name Instructor Time your class meets MATH 202- MIDTERM EXAM Wednesday, March 10, 2004, 7:30PM-9:00PM McCosh 10 Average was 51 1. (16 points) The linear transformation T transforms vectors in R 2 in the following way: first it rotates the vector through an angle of 30 degrees counterclockwise about the origin, then it doubles the vectors length and then it reflects the resulting vector across the line of slope 1 through the origin. What is the standard matrix of T ? 2. (16 points) Let A = 1 2 2 1 3- 1- 2 1 1 2 4- 1 1 which row reduces to rref ( A ) = 1 2 2 1 3 . (a) Find a basis for the image of A . (b) Find a basis for the kernel of A . (c) Find a matrix B such that the image of B is the same as the kernel of A . (d) Find a matrix C such that the kernel of C is the same as the image of A . 3. (16 points) Let V be the subspace of R 4 spanned by the vectors ~v 1 = 1 1 1 1...
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