MATLAB: Left matrix multiplication giving wrong answer (off by 0.125)

left matrix multiplication

When I have
A= [   0.401792457631424   0.095713396253060   0.115003590060302
  -0.118005996178075  -0.395819173484325   0.252104651817522
  -0.283786461453348   0.300105777231265  -0.367108241877824];
b=[1; 0; 0];
x=A\b;
when I take
A*x
I don't get b back:
>> A*x
ans =
   1.000000000000000
   0.125000000000000
                   0
Does anyone have any ideas on what could be wrong here?
The problem persists if I use e.g. b=[1.000000000001; 0; 0], though in that case I get
>> A*x
ans =
   0.968750000000000
   0.125000000000000
   0.125000000000000

Best Answer

rank(A)
 % ans = 2
shows that there are only two linearly independent rows of A, it ideally would be 3 for a 3x3 matrix.
doc rank
for more info.
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