MATH 310 Midterm: Math 310 Exam 2 1
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1 1 1 (a) [10] compute an lu decomposition for a. (b) [10] what is the determinant of a: consider the matrix. What are the dimensions of the three subspaces? (include the dimension of the one for which you did not nd a basis. ) (c) [10] let b be the basis for row c that you found in part (b). Another basis c is given by the two vectors c1 = 4. (a) [10] use cofactor expansion to compute the determinant of. 5. (a) [10] a markov process is de ned by the stochastic matrix. 0. 5(cid:21)? (in other words, what vector does m n x0 if x0 = (cid:20)0. 5 x0. What is limn m n approach when n is very large?) (b) [10] consider the three polynomials p1(t) = 1 + t, p2(t) = 1 + 2t, p3(t) = 2 + 3t.
