- #1
sassie
- 35
- 0
Homework Statement
Let A and B be vector spaces, T:A->B be a linear transformation.
Give examples of:
(a) T, where a(1),... a(n) are linearly independent vectors in A, but T(a(1)),...T(a(n)) are not.
(b) T, where T(a(1)),...T(a(n)) span the range of T, but a(1),... a(n) do not span A.
Homework Equations
My ideas were to think about onto and 1-to-1-ness. (e.g. T is 1-to-1 iff the columns of the standard associated matrix T are linearly independent). However, I'm not 100% sure because the equations I have don't really make sure, and I'm not sure whether they apply to vector spaces.
The Attempt at a Solution
Let T be:
(a) [1 2 4 0
2 0 2 0
3 1 1 0]
(b) [1 2 3
0 2 5
0 0 2
0 0 0]