Question

I have simple question in matlab.
I have the equation : A*H=b
I know A and b
I try to use this expression:

H=A\b;

but I get wrong value: example:

       A =

       231   481
       233   488
       241   481
       243   489
b =

    11    31
     6    20
    21    31
    18    22

And I get

H =

    1.1627    0.2713
   -0.5396   -0.0791

so

A*H

ans =

    9.0386   24.6299
    7.5868   24.6189
   20.6659   27.3434
   18.6745   27.2532

This is no b

Answer 1

From typing help slash at the command prompt:

\ Backslash or left division.

A\B is the matrix division of A into B, which is roughly the same as
INV(A)*B , except it is computed in a different way. If A is an N-by-N
matrix and B is a column vector with N components, or a matrix with
several such columns, then X = A\B is the solution to the equation A*X
= B. A warning message is printed if A is badly scaled or nearly singular. A\EYE(SIZE(A)) produces the inverse of A.

If A is an M-by-N matrix with M < or > N and B is a column vector with M
components, or a matrix with several such columns, then X = A\B is the
solution in the least squares sense to the under- or overdetermined
system of equations A*X = B. The effective rank, K, of A is determined
from the QR decomposition with pivoting. A solution X is computed
which has at most K nonzero components per column. If K < N this will
usually not be the same solution as PINV(A)*B. A\EYE(SIZE(A))
produces a generalized inverse of A.

So, the second paragraph applies to your case. In other words, there is no H that can satisfy A*H = b for your problem, but Matlab computes the best approximation to it (in a least-squares sense). So the result you get is correct.