2. (12 points) Consider the linear system x1 + X2 + ax₂ I1 2x1 + 2x₂ x1 + 12 bx3 + (b-a)™₁ bx3 bx3 + ax4 = b-2 = 1 = 0 0 for some real numbers a, b € R. (a) Determine the values of a and b such that the system has no solution. (b) Determine the values of a and b such that the system has only one solution. Write down the unique solution. (c) Determine the values of a and b such that the system has infinitely many solutions with 1 parameter in the general solution. Write down the general solution. (d) Is it possible for the system to have infinitely many solutions with 2 parameters in the general solution? Explain your answer. Show all your elementary row operations used clearly.

Fig: 1