WI08Session 2inverses -Jan16

WI08Session 2inverses -Jan16 - mma2.txt Mathematica Session...

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mma2.txt Mathematica Session 2 Math 1b January 16, 2009 On the next page, we calculate the inverse of a "random" 5 by 5 matrix. On the following pages, we try to find a nonnegative solution to a system of linear equations Ax = b . We fail. But by carrying along an identity matrix in our computations, we produce a vector y so that yA >= 0 but yb < 0 . Page 1
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rand @ m _ ,n _ D : = Table @ RandomInteger @ 10 D , 8 i, m < , 8 j, n <D AA = A = rand @ 5, 5 D ; MatrixForm @ A D 81 0845 81647 31 0649 10 1 3 8 2 20554 Do @ AA @@ i DD = Join @ AA @@ i DD , IdentityMatrix @ 5 D@@ i DD D , 8 i, 5 <D ; MatrixForm @ AA D 8 1 084510000 8 1 64701000 3 1 064900100 1 01 38200010 2 0 55400001 AA = RowReduce @ AA D ; MatrixForm @ AA D 10000 389 16115 1538 16 115 611 16115 62 1465 2144 16115 01000 711 16115 1373 16115 996 16115 38 1465 936 16115 00100 2631 16115 87 16 115 2434 16115 187 1465 3064 16 115 00010 201 3223 455 3223 208 3223 35 293 387 3223 00001 2227 16 115 1966 16 115 2048 16115 16 1465 1148 16115 B = AA @@ 8 1, 2, 3, 4, 5 < , 8 6, 7, 8, 9, 10 <DD ; MatrixForm @ B D 389 16 115 1538 16115 611 16115 62 1465 2144 16115 711 16 115 1373 16 115 996 16 115 38 1465 936 16115 2631 16 115 87 16115 2434 16115 187 1465 3064 16115 201 3223 455 3223 208 3223 35 293 387 3223 2227 16115 1966 16115 2048 16 115 16 1465 1148 16115 B.A 88 1, 0, 0, 0, 0 < , 8 0, 1, 0, 0, 0 < , 8 0, 0, 1, 0, 0 < , 8 0, 0, 0, 1, 0 < , 8
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WI08Session 2inverses -Jan16 - mma2.txt Mathematica Session...

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