Ax=b solution with singular matrix.

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sermet 2013-12-3

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https://ww2.mathworks.cn/matlabcentral/answers/108418-ax-b-solution-with-singular-matrix

评论： Roger Stafford 2013-12-3

采纳的回答： Matt J

%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 2013-12-3

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https://ww2.mathworks.cn/matlabcentral/answers/108418-ax-b-solution-with-singular-matrix#answer_117114

在 MATLAB Online 中打开

pinv(A)*b

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sermet 2013-12-3

ok, Roger, thank you I just made mistake.

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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