Homework Help: Nullity Question

1. Oct 10, 2008

_F_

1. The problem statement, all variables and given/known data
Find the nullity of the linear transformation T:M_2x3(F) -> M_2x2(F) defined by:

T([a11, a12, a13; a21, a22, a23]) = ([2*a11 - a12, a13 + 2*a12; 0, 0])

3. The attempt at a solution
N(T) = {x in M_2x3(F) | T(x) = 0}

2*a11 - a12 = 0 => a11 = (a12)/2
a13 + 2*12 = 0 a13 = -2*a12

N(T) = {[a/2, a, -2*a; 0, 0, 0] | a in F}

Basis(N(T)) = {[1/2 1 -2; 0, 0, 0]}

nullity(T) = 6

But nullity(T) should be 4...

Any help is appreciated.

2. Oct 10, 2008

Defennder

Why are these entries 0's? Look at the formula given for T. Do a21,a22,a23 appear anywhere in the transformed 2x2 matrix?

3. Oct 11, 2008

_F_

You're right. But that said, if you take away the zero's you still get a 1x3 matrix whose dimension is 3...

4. Oct 11, 2008

Defennder

You meant I a 2x3 matrix I presume. And it doesn't make sense to talk about the dimension of a matrix. You meant the dimension of the nullspace. And it isn't 3. How did you arrive at that?