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Unformatted text preview: MATH 202  Midterm Exam October 24, 2007 (90 minutes) Average was 62 points. 1. (20 points) A = 1 2 1 1 1 2 4 1 5 0 3 6 2 6 6 0 0 2 6 7 row reduces to rref ( A ) = 1 2 0 4 0 0 0 1 3 0 0 0 0 0 1 0 0 0 0 0 (a) Find a basis for the kernel of A . (b) Find a basis for the image of A . (c) The vector b = 3 3 11 9 in the image of A . Find its coordinates with respect to your basis in part (b). (d) Find the general solution to the linear system A x = b where b is the vector in part (c). 2. (20 points) Consider the plane V in R 3 defined by the equation 2 x 1 x 2 + 5 x 3 = 0. (a) Find a basis for V . (b) Find a basis for V . (c) Find the matrix for projection onto V (in standard coordinates). (d) Find the matrix for reflection across V (in standard coordinates). 3. (20 points) Let V be the subspace of R 4 with basis v 1 = 1 1...
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 Spring '08
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 Math, Linear Algebra, Algebra

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