The extended matrix of the system is


    .



(a)  the system has infinitely many solutions, if and only if both lines of the coefficient matrix are proportional.


     From the form of the matrix, it is clear that the only value of "t" for it is  t= 0.



(b)  For all other values of "t" the lines of the matrix are not proportional

     Hence, for all values of "t" different from t= 0, the system has a unique solution.



(c)  In part (b),  there are infinitely many possible values of "t".