(123)x=a (456)y=b (789)z=c For which values (a,b,c) does the above equation have a solution where a,b,c,x,y,z belong to R? Initially I found the determinant of the above matrix and it was O. From this I know that there will be nontrivial solution solutions for (a,b,c) = (0,0,0). But I am confused as to the possibility of having any other solutions for nonhomogenous system. I know that it will not have a uniques solution. Can any body tell me if there is going to be any other solutions for values of (a,b,c) other than the homogenous one.