Matrix multiplied by inverse is not giving correct answer

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Raja Dawn
Raja Dawn 2020-7-26
回答： David Goodmanson 2020-7-26
The inverse of a matrix multiplied by itsef should give an identity matrix but the result I get is this: [0 0 0; -4 0 0; -4 0 0]
  1 个评论
Vladimir Sovkov
Vladimir Sovkov 2020-7-26
Try
det(sym(a))
It is strict zero. Hence, there is no inverse matrix indeed. Matlab is quite correct here.

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回答（1 个）

David Goodmanson
David Goodmanson 2020-7-26
Matlab is telling you the answer, that the matrix (call it M) is close to singular or badly scaled (singular in this case). M has a ridiculously small condition number of 2e-18. It doesn't have an inverse, and the one it comes up with is due to numerical precision issues.
If M had an inverse, it would be impossible to have a nonzero column vector u such that M*u = 0. However,
M = [1 2 3;4 5 6;7 8 9]
M*[1; -2; 1]
ans =
0
0
0

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