MATH-205 Midterm: Bates MATH 205 121506jayawant205exam
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Name: check that you have 10 questions on ve pages, show all your work to receive full credit for a problem, (18 points) short answers: (no explanations needed. If you do some calculation to get the answer, show the calculation. ) (a) (6 points) let a and b be 4 4 matrices, with det a = 4 and det b = 7. Find ~q in p2, given that [q]b = . 1 (c) find the coordinate vector of ~p(t) = 3 t + 7t2 relative to b: (8 points) a quadratic form on r2 is given by the formula q(x1, x2) = 8x1x2 6x2. 2. (a) find the matrix a of the quadratic form. (b) classify the quadratic form: (12 points) determine if the following sets are subspaces of the appropriate vector spaces. If a set is a subspace, nd a basis and the dimension of the subspace.
