I have a question regarding linear algebra which I am unsure of how to approach. The question says:
Determine the values of a for which the following system of equations has (a) no solutions, (b) exactly one solution, and (c) infinitely many solutions.
x + y + 7z = -7
2x + 3y + 17z = -16
x + 2y + (a^2+1)z = 3a
So I assume that we would use some form of Gaussian to figure out the solutions because thats what have have been doing in the course so far, but everything I have tried so far has failed!!!
I did get a solution of a=3 for no solutions, but I'm not actually sure if this is correct (what I did was set a^2-6 equal to 3 after using row reduction). Anyway any help I could get would be greatly appreciated or even just any clues as to how I should start this problem.
Thanks in advance!!