Confusion related to lsqr linear equation solver of matlab

Question

I have this confusion related to the lsqr linear equation solver in matlab. It states that x = lsqr(A,b) attempts to solve the system of linear equations A*x=b for x if A is consistent. I didn't get what they mean by consistent. Can anyone explain?

Answer 1

It means that the system of equations has a solution. Consider the alternative case which is inconsistent - this would be a system of equations that has NO solution. For a simple example, finding the intersection point of a pair of (non-identical) parallel lines in the plane - this would be described by an inconsistent system of equations. See this for a fuller explanation http://en.wikipedia.org/wiki/System_of_linear_equations#Consistency

Answer 2

一致==它至少有一个解决方案