(0,0) must be in X(why?)! Hence a*0+b*0+c!=0 - absurd!
Here attached is the question:
How do I prove it as an if and only statement.
We have learnt the definition of subspace being when the set is empty, closed under vector addition and closed under multiplication.
I can prove for when c=0 that it is a subspace. How do I prove for all other values, that it is not a subspace?