(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Nullity Question

**Physics Forums | Science Articles, Homework Help, Discussion**