Using conditionals to check if LinearSolve found a solution

Question

Is there some way to check if LinearSolve found a solution using conditionals in Mathematica 9? I need to solve a large number of linear equations, but I am only interested in the cases where there actually is a solution.

If there is no solution for the equation $Ax=b$, the output of LinearSolve will be

LinearSolve[A,b],

but I do not know how to exploit this.

Edit: I found a solution which should work with Mathematica 10:

StringFreeQ[TextString[LinearSolve[A,b]],LinearSolve]

first converts

LinearSolve[A,b]

into a string and then checks whether LinearSolve is part of that string. However, TextString only works with Mathematica 10 to which I do not have access.

Answer 1

LinearSolve will generate an error message when it fail. Hence you can catch those messages. Number of ways to do this. Here is an example.

mat = {{0, 0}, {0, 0}};
b = {1, 0};
status = True;
status = Check[LinearSolve[mat, b], False, LinearSolve::nosol]

(* False*)

So status can be checked for False. If it is not False, then it passed. So simply set status=False before the call, and after the call do something like If[Not[status]],... etc...

No need to using strings and all of that.

reference: http://reference.wolfram.com/language/ref/Check.html

Answer 2

checking the Head is another way, useful in a construct like this:

 alist = {{{1, 0}, {0, 1}}, {{0, 0}, {0, 0}}};
 Quiet@Select[  
    {#, LinearSolve[#, {1, 0}] } & /@ alist , Head@#[[2]] == List & 

{{{{1, 0}, {0, 1}}, {1, 0}}}