MATH 1502 Midterm: MATH 1502 GT C2T401sol
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I: a) false, b) true, c) false, d) false, e) false, f) true, g) false. ~v1 = 2~u1 ~v2 = (~u1 ~v2)~u1 + (~u2 ~v2)~u2 = 2~u1 + 12/ 6~u2. A = qr where q = [~u1, ~u2] and r = (cid:20) 2. Iii: a) ker(a) is given by all the multiples of the vector. 1 (1: the vector given in (1) is a basis for ker(a), img(a) is given by the plane x + y 3z = 0 , a basis for this plane is given by the vectors. Iv: a) the given set is a subspace: the orthogonal complement s is given by all the multiples of the vector c) 1: since s and s are complementary, we have that ps + ps = i and hence. 1 1 1: the distance is given by the length of the vector ps ~a.
