- #1

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## 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]