What exactly are you trying to compute? You can definitely multiply vectors by matrices, that is how you compute vertex positions and many things in shaders. Or is there something special you are trying to do, I don't quite understand the question.
mat4 myMatrix;
vec4 myVector;
// fill myMatrix and myVector somehow
vec4 transformedVector = myMatrix * myVector;
http://www.opengl-tutorial.org/beginners-tutorials/tutorial-3-matrices/