MATLAB: Matlab, operator A/B

?operation a/brow vector

The manual is written:
A\B returns a least-squares solution to the system of equations A*x= B.
It means: x = inv (A'*A)*A'*B? However, the matrix A'*A is singular…
Let us suppose to have two row vectors:
A=[1 2 3]
B=[6 7 6]
A\B
 [0         0         0;
  0         0         0;
  2.0000    2.3333    2.0000]
If ve use MLS:
C = inv (A'*A)   singular matrix
C = pinv(A'*A)
[0.0051    0.0102    0.0153
 0.0102    0.0204    0.0306
 0.0153    0.0306    0.0459]
And
D= C*A'*B
[0.4286    0.5000    0.4286
 0.8571    1.0000    0.8571
 1.2857    1.5000    1.2857]
So results A\B and inv (A'*A)*A'*B are different… Could anybody wrote me a sequence of Matlab commands in the backgeound of A/B operation in this case?

Best Answer

When A is singular there are infinite least squares solutions to A*X=B and A\B will pick just one of them, while pinv(A)*B picks another.
A/B is equivalent to (B'\A')'
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