Linear Algebra/Matrices to solve Linear System

Question

Consider the linear system with 4 unknown variables x1, x2, x3, x4 and 4 equations.

x1 + x2 - bx3 + (b-a)x4 = b-2

x1 + ax2 - bx3 = 1

2x1 + 2x2 + ax4 = 0

x1 + x2 - bx3 = 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.

Preferably full solutions so I can understand each step! I got the linear system to REF form, but don't know how to continue afterwords. Thanks!

Answer 1