Find conditions on a such that the following linear system has no solution, exactly one solution, or inﬁnitely many solutions. In the case when the system has a unique solution, ﬁnd the solution in terms of a.
The system of equations given is as follows:
x + z = -1
4x + 4y + az = 0
-4x-ay-(a+4)z = -4
The solution I got was as follows:
i. The system has no solution when a = 0. ii. The system has infinite solutions when a = 8. iii. The system has a unique solution a is not equal to 8 or 0.
However, for the second part of the question I do not know how to express the unique solution in terms of a. Could I perhaps receive some help on this and also on checking through my answer?