- #1
GlassBones
- 16
- 1
Homework Statement
Let ##T:V \rightarrow W## be an ismorphism. Let ##\{v_1, ..., v_k\}## be a subset of V. Prove that ##\{v_1, ..., v_k\}## is a linearly independent set if and only if ##\{T(v_1), ... , T(v_2)\}## is a linearly independent set.
Homework Equations
The Attempt at a Solution
[/B]
##\rightarrow##: I began with the definition of linear independent vectors.
But I realized this could map to vectors that become dependent vectors in ##W##.
I suppose the fact that T is an isomorphism is a hint. Can anyone give me ideas?
Last edited: