MATH235 Final: A3
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20 Jun 2019
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Due: wednesday oct 7th: the vector space s = {a m2 2(r) | a(cid:20)1 1. U = {p(x) p2(r) | p(1) = 0}. M : v w be one-to-one linear mappings. If u and w are isomorphic, prove that. V is isomorphic to u: prove or disprove the following statements. (a) let l : v u and m : u w be linear mappings. If m l is one-to-one, then l is one-to-one. (b) let l : v u and m : u w be linear mappings. If m l is one-to-one, then m is one-to-one. (c) let m : v w be an onto linear mapping. , ~x } spans v, then: let t : v v be a linear mapping and let b = {~v1, . , ~vn} be a basis for v such that. , ~vn} is a basis for ker(t ).