MATH 308 Final: Final Exam 2
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(1) (question from toby johnson, winter 2011) (a) (6 points) let ~w1 = . Find an (b) (4 points) let s = {~u1, ~u2} be the orthonormal basis you found in part(a). As a linear combination of ~u1 and ~u2. (2) (question from toby johnson, winter 2011) Let a be a 3 2 matrix such that. 4 (cid:19) ? (a) (2 points) what is a(cid:18) 2 (b) (5 points) what is a(cid:18) 2. 1 (c) (3 points) what is the dimension of range(a) ? (3) (10 points) (question from lindsay erickson, winter 2011) Find a basis for the following vector space. T ~x = a~x, satis es the following properties. 0 (6) (10 points) let a be a 3 3 matrix such that the algebraic multiplicity of the eigenvalue. Determine the geometric multiplicity of the eigenvalues = 1 and = 1. (i) (4 points) let a be a 3 3 matrix.
