Let T: V -> V be a linear operator.
• Prove that if T is injective and {vi} is linearly independent, then {Tvi} is also linearly independent.
• Prove that if T is surjective and {vi} spans
V, then {Tv} also spans V.
Mathbot Says...
I wasn't able to parse your question, but the HE.NET team is hard at work making me smarter.