Can MATLAB help solve a matrix that contains only variables

I am aware of MATLAB being able to solve matrices but will it produce a solution if the matrices only contain variable e.g. [a b c;d e f;g h i]*[x y z]=[0 0 0]?

Answer 1

[Walter Roberson]

It will only be able to find a non-trivial null vector if the rank of the symbolic matrix can be determined to be less than the maximum dimension of the matrix. If the 3 x 3 has only different symbol names rather than formulae that might be reduced, and there are no active "assumptions" that could be used to make deductions, then it would not be able to find a non-trivial null vector.