MATH-205 Midterm: Bates MATH 205 041609jayawant205exam
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Name: check that you have 8 questions on four pages, show all your work to receive full credit for a problem, (12 points) short answers: (show all the calculations to get the answers. What is the smallest possible dimension of nul c? (b) for a 3 3 matrix b, det b = 1. Find det 4b. (c) find the distance between the vector ~u = (cid:20) 3. 1 (cid:21) and the vector ~v = (cid:20) 1. 1 (cid:21). (d) let t : r3 r2 be the linear transformation given by. T (x1, x2, x3) = (x1 x2, 2x2 x3). Find a matrix a such that t (~x) = a~x. (e) let ~p1(t) = 1, ~p2(t) = 2t, ~p3(t) = 4t2 2 and ~p4(t) = 8t3 12t. Then b ={~p1, ~p2, ~p3, ~p4} is a basis for p3. Find the polynomial ~q in p3, given that [q]b =
