MATH 4130 Midterm: Exam1_Math413_Fall2010
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Part i (60%) - in class: oct 6, 2010. Part ii (40%)- take home: due monday, oct 11, 2010 at 4:30pm: problem 1. For each of the following statements, give either a short proof (if the statement is true) or a counterexample (if the statement is false) If s1 and s2 are subsets of a vector space v then span(s1) span(s2) span(s1 s2) The set {a mn n(f)|a2 = 0} is a subspace of mn n(f). The map t : p (r) p (r), which maps a polynomial p(x) to p(x2), is linear. [e. g. t (1 + 3x + x2) = 1 + 3x2 + (x2)2 = 1 + 3x2 + x4] . The vector spaces f4 and m2 2(f) are isomorphic. 1: problem 2 find a basis for the following subspace of r5: W = {(a1, a2, a3, a4, a5) r5 : a1 = a3 = a4 and a2 + a5 = 0}.
