MATH-205 Midterm: Bates MATH 205 032404greer205exam
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While the nal answer is important, you earn points for all the work leading to that answer, as well as the answer itself. Show all your steps clearly so you will be eligible for the most partial credit. Determine whether the set of polynomials {3 + 7t, 5 + t 2t3, t 2t2, 1 + 16t . 6t2 + 2t3} forms a basis for p3. Find the coordinate vector [x]b of x = . Nd a basis, and s 2t s + t. : s, t in r b. ) state the dimension. , compute r s r r r. Find the characteristic polynomial and the eigenvalues of the matrix . Let a be an n n matrix. True or false: an eigenspace of a is a null space of a certain matrix. If false: explain why in detail, and/or provide a counterexample, that is, an example to show when the statement is false.
