# Homework Help: Basis for nullspace of T

1. Oct 29, 2012

### charlies1902

The problem is attached.

I am instructed to find a basis for the nullspace of T.

A basis for a 2x2 matrix is
1 0
0 0

0 1
0 0

0 0
1 0

0 0
0 1

Applying the transformation to each of these gives
0 0
0 0

0 2
0 0

0 0
-2 0

0 0
0 0
respectively.

Now this is where I get stuck. How do I find a basis after knowing these 4 matrices?

It look like it's a linear combo of 2 matrices:
0 1
0 0
and
0 0
1 0

but the answer in the book is
1 0
0 0

0 0
0 1

I don't undertand.

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Last edited: Oct 29, 2012
2. Oct 29, 2012

### Staff: Mentor

Which matrices get sent to (transformed to) the zero matrix? That's the basis for Null(T).

3. Oct 29, 2012

### charlies1902

Gotcha, I keep it getting it cnofused with range (T), nullspace(T) is solved by setting the right hand side of the transformation equal to 0 right?

So for this case,
0 1
0 0
and
0 0
1 0

would be a basis for the range of T?

4. Oct 29, 2012

### Staff: Mentor

I think so, but I didn't check your work.