I have two matrices:
A = [ -1 0 0; 1 1 -1; 0 -1 1 ]; B = [-1; 0; 1];
and I want to solve the following equation:
Ax=B
when I use mldivide
function I get a matrix of NaNs
X = mldivide(A,B) X = NaN NaN NaN
Knowing there are multiple solutions to this problem I manually tested if one of them, namely [1;0;1]
returns B
:
A*[1; 0; 1]
and, as expected, I reassured myself that it is one of multiple solutions. So here is my question: why does mldivide
return incorret solution?
Your matrix A is singular. The MATLAB doc states that in these cases, mldivide is unreliable ("... When working with ill-conditioned matrices, an unreliable solution can result ...") and suggests to use lsqminnorm( ) or pinv( ) instead (see "Tips"). E.g.,
>> A = [ -1 0 0; 1 1 -1; 0 -1 1 ]; >> B = [-1; 0; 1]; >> A\B Warning: Matrix is singular to working precision. ans = NaN NaN NaN >> A*ans-B ans = NaN NaN NaN >> lsqminnorm(A,B) ans = 1.0000 -0.5000 0.5000 >> A*ans-B ans = 1.0e-15 * 0.4441 -0.3331 -0.1110 >> pinv(A)*B ans = 1.0000 -0.5000 0.5000 >> A*ans-B ans = 1.0e-15 * 0.2220 -0.4441 0.2220
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