MATH-205 Midterm: Bates MATH 205 031811jayawant205exam
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Use properties of determinants to compute: (a) det 2a (b) det b: (4 points) let h = span {~v1, ~v2, . Explain: (6 points) suppose ~u is an eigenvector of a 4 4 matrix a corresponding to the eigenvalue. Explain. (b) show that ~u is an eigenvector of a3 and nd the corresponding eigenvalue: (4 points) determine if the following set is a subspace of the appropriate space. If the set is a subspace, nd a basis and the dimension of the subspace. If the set is not a subspace, provide a counterexample to illustrate that one of the conditions in the de nition of subspace does not hold. W = (cid:26)(cid:20) a (cid:21) where a, b are non-negative real numbers(cid:27) . And let ~w = : (8 points) let ~v = . ~v ~v (cid:19) ~v and call it ~y. (a) compute (cid:18)~v ~w. 0 (b) compute ~w ~y and call it ~z. (c) let l = span{~v}.
