For which value(s) of k ∈ R, if any, will the following system have (a) no solution, (b) a unique solution, (c) infinitely many solutions
x − 2y + 3z = 2
x + y + z = k
2x − y + 4z = k2
Here is an excellent video, with diagrams and example set of equations.
There are actually 3 videos, they should run into each other.
https://www.youtube.com/watch?v=duFRYId7kNU