# Give an example of a linear transformation

## Homework Statement

Give an example of a linear transformation whose kernel is the line spanned by:

-1
1
2

in lR³

Would:

1..(-1)...0
0....0.....0
0..(-2)...1

be a solution?

## Answers and Replies

To prove it, prove your vector is in the kernel and that the dimension of the col. space is 3 - nullity = 2.

HallsofIvy
Science Advisor
Homework Helper
It quite obviously isn't since Av is not 0. Are you clear on the definition of "kernel"?

Actually your matrix has only a single entry wrong so it may be just a typo.