find the inverse of

A=[1 5 -2]

     [3 -1 4]

     [-3 6 -7]
asked Nov 12, 2016 in Other Math Topics by anonymous

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1 Answer

I take A to be a matrix.

Determinant=1(7-24)-5(-21+12)-2(18-3)=-17+45-30=-2.

Reorientate:

[1 3 -3]

[5 -1 6]

[-2 4 -7]

Now we find the elements of a new matrix:

[(7-24) (-35+12) (20-2)]

[(-21+12) (-7-6) (4+6)] =

[(18-3) (6+15) (-1-15)]

[-17 -23 18]

[-9 -13 10]

[15 21 -16]

Now apply the signs matrix:

[-17 23 18]

[9 -13 -10]

[15 -21 -16]

Now divide by the determinant -2:

     [8.5 -11.5 -9]

B=[-4.5 6.5 5]

     [-7.5 10.5 8]

If this is correct (!) then A x B=I:

[1 5 -2][8.5 -11.5 -9]

[3 -1 4][-4.5 6.5 5] =

[-3 6 -7][-7.5 10.5 8]

[1 0 0]

[0 1 0]

[0 0 1]

Looks like we struck lucky!
answered Nov 13, 2016 by Rod Top Rated User (429,280 points)
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