I don't know how to because I haven't done one before. My teacher writes definitions on the board and proofs, but no practical examples, so nothing is cementing in my brain.
Homework Statement
Prove: If V and W are finite-dimensional vector spaces such that dim(W)<dim(V), then there is no one-to-one linear transformation T:V-->W
The Attempt at a Solution
I don't know how to do a well thought out proof.
Determine whether the linear transformation T is one-to-one
a) T:P2 --> P3, where T(a+a1x+a2x^2)=x(a+a1x+a2x^2)
b) T:P2 --> P2, where T(p(x))=p(x+1)
I'm having difficulty because my teacher never showed examples like this one.
Please help me on the procedure and solution.