solve A*x=B

size of A is 566*664 and B is 566*1.......I tried every function like mldivide, A\b, linsolve but after getting x, when I multiply A with x it does not give me B Matrix.....What should be the reason? Is matrix wrong?

Please note that Rank of Matrix A is 461

Answer 1

[James Tursa]

Sounds like you have inconsistent equations. The A\B calculation is doing the best that it can under these circumstances. E.g.,

>> A = [1 2 3;2 4 6]  % <-- 2nd row is 2*1st row, so rank deficient
A =
     1     2     3
     2     4     6
>> B = [1;2]  % <-- this particular B is consistent with both rows of A
B =
     1
     2
>> x = A\B
Warning: Rank deficient, rank = 1,  tol =   4.4686e-015. 
x =
         0
         0
    0.3333
>> A*x  % <-- works because equations are consistent
ans =
     1
     2
>> 
>> B = [1;3]  % <-- this particular B is not consistent with the rows of A
B =
     1
     3
>> x = A\B
Warning: Rank deficient, rank = 1,  tol =   4.4686e-015. 
x =
         0
         0
    0.4667
>> A*x  % <-- does not work because of the inconsistency. This is the best that backslash can do
ans =
    1.4000
    2.8000

How are your A and B variables being calculated?

[KALYAN ACHARJYA]

@James Thanks Sir, I missed it.

Thanks for pointing out the error.

[Sajjad Malik]

Thanks James Tursa for reply Actually I am trying to solve an optimisation problem I have mathematical equations from which I got A and B values it is a chance that equations are wrong but still I wonder why I did not get the actual values of B matrix ? because I get unknown matrix x using A\B

[James Tursa]

Look at my examples closely. When you have dependencies in the equations then you will need to have consistent right-hand-side values to match those dependencies in order to be able to find a solution. In my first example I did have that and I was able to find a solution such that A*x matched the B result. But in my second example the B values were not consistent with the dependencies in the A matrix. In this case the A\B is doing the best that it can, but it can't give you what you want because you didn't give it a system that could be solved like you want. It appears to me that this is what might be going on in your system of equations. You have dependencies among them (you admit that up front because your system is rank deficient), but the right-hand-side B values for these dependencies are not consistent. At least not consistent enough for you to get an answer that you are willing to accept.

[Sajjad Malik]

Thank you James. I got your point.Regards