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- %% Problem 4
- P = [.9 .01 .09, .01 .9 .01, .09 .09 .9]
- sump = sum(P)
- % a) P is a stochastic matrix, as all of its rows and columns add up to 1 and
- % each element is at least zero.
- %b)The equation Pq=q tells us that if one of the eigen values is 1,
- % the others do not matter.
- %c)Using the eig function on P yields in the following values:
- %0.4354
- %0.0909
- %0.4737
- %[V,D] = eig(P)
- %d)
- v=eig(sump)
- %e) About 182 cars will be rented from the downtown location
- % 2000 * .0909
- %% Problem 5
- a=7
- b= -8
- c = 1
- C = [a -b, b a]
- E = [a -b, b a]
- D = [c 0, 0 c]
- factC = lu(C)
- factE = qz(E,D)
- %I used LU factorization for C and QZ factorization for E.
- %You can obtain both types of factorization for the same matrix.
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