MATH-205 Midterm: Bates MATH 205 121013buell205exam
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Read all of the following information before starting the exam: show all work clearly in the blue book in order to get full credit. 0: (2 pts) what is the dimension of the subspace w spanned by the columns of a, (11 points) let a = (cid:20) 2 3. Diagonalize a in two ways. (diagonalization is not unique, so give two possible ways it could be done. : (3 pts) Explain how you can determine a20 using one of the decompositions from above: (6 points) suppose b is a 5 5 matrix. Use coordinate vectors to show that these polynomials form a basis for p2. Consider the basis = {~p1, ~p2, ~p3} for p2. Find ~q in p2 given that [~q] = . 2: (9 points) orthogonal diagonalization, (5 pts) Show that if a is orthogonally diagonalizable, then a2 is also orthogonally diagonal- izable: (4 pts)
