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MATLAB HW4

# MATLAB HW4 - Section B05 Nicholas Nguyen 4.1 a > A...

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Section B05 Nicholas Nguyen 4.1 a) >> A = [8,11,2,8;0,-7,2,-1;-3,-7,2,1;1,1,2,4] A = 8 11 2 8 0 -7 2 -1 -3 -7 2 1 1 1 2 4 >> B = [1,-2,0,5;0,7,1,5;0,4,4,0;0,0,0,2] B = 1 -2 0 5 0 7 1 5 0 4 4 0 0 0 0 2 >> C = A+B C = 9 9 2 13 0 0 3 4 -3 -3 6 1 1 1 2 6 >> det(C) ans = 0 >> C = A-B C = 7 13 2 3 0 -14 1 -6 -3 -11 -2 1 1 1 2 2 >> det(C)

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ans = 1.0380e+003 >> C = A*B C = 8 69 19 111 0 -41 1 -37 -3 -35 1 -48 1 13 9 18 >> det(C) ans = 3.6480e+003 >> det(A^-1) ans = 0.0132 >> det(B') ans = 48 b) A+B is not invertible because the row reduced echelon form of it has a free variable and matrices with free variables are not invertible. c) We can still calculate det(AB) since det(AB) = det(A) * det(B). We can also calculate det(A -1 ) since det(A -1 ) = (det(A)) -1 . We can also calculate det(B T ) since det(B T ) = det(B). 4.2 >> N = [.02,.003,0;1,.01,0;0,0,.005] N = 0.0200 0.0030 0 1.0000 0.0100 0 0 0 0.0050
>> det(N^100) ans = 0 N 100 is not invertible because the row reduced echelon form of it has 2 free variables. >> det(N) ans = -1.4000e-005 -1.4000e-005 ^100 = (-1.4)^100 * (10^-5)^100 = (4.1e14) * (e-500) = 4.1e486 which is not 0 but very close to 0. This is explained in remark 4.1 about the rounding errors that MATLAB has. I would still not reconsider my answer on if N 100 is invertible or not because of the row reduced

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MATLAB HW4 - Section B05 Nicholas Nguyen 4.1 a > A...

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