Consider the following system of linear equations in variables $x_1, x_2, x_3,$ where $a,b$ are some fixed real numbers.
$$x_1+x_2-x_3 = 1$$
$$2x_1+x_3 = 1$$
$$x_1-ax_2 + 2x_3 = b$$
Find the values of $a,b$ for which the system has: (i) infinitely many solutions, (ii) exactly one solution, (iii) no solutions.
Does anyone have an, idea of how I should approach this exercise. I tried to reduce the matrix.