find the values of p for which the system has a no solution

find the value(s) of p for which the system has (a) no solution, (b) unique solution, (c) infinitley many solutions. in case (c), if p has a unique value, write down the general solution to the system.

x₁ - 2x₂ + 3x₃ = 1

2x₁ + px₂ +6x₃ = 6

-x₁ + 3x₂ + (p - 3)x₃ = 0

Solution

x1 - 2x2 + 3x3 = 1
2x1 + px2 +6x3 = 6
-x1 + 3x2 + (p - 3)x3 = 0