Ax=b solution with singular matrix.

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sermet
sermet 2013-12-3
评论： Roger Stafford 2013-12-3
%x+2y+3z=14
%4x+5y+6z=32
%7x+8y+9z=41
(actually, x=1,y=2,z=3)
A=[1 2 3;4 5 6;7 8 9]
b=[14;32;41]
x=A\b
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.093272e-16.
%in order to eliminate this singularity singular value decomposition strongly recommended.
How can I perform svd for solving this equation properly?

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Matt J
Matt J 2013-12-3
pinv(A)*b
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sermet
sermet 2013-12-3
ok, Roger, thank you I just made mistake.
Roger Stafford
Roger Stafford 2013-12-3
A geometrical interpretation of these equations would be that they each represent a plane in 3D. Two of the planes intersect in a line, and the third plane is parallel to this line, but never intersects it, so the three planes never have a common intersection. Even trying to find a "best solution" has no unique answer - all points along a certain infinite line would have the same least squares error.

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