(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given transformations T_1, T_2:V->F where V is a vector space with the dimension n over the field F, T_1 , T_2 =/= 0. If N_1 = KerT_1 , N_2 = KerT_2 and N_1 =/= N_2 find dim(N_1 intersection N_2)

2. Relevant equations

dim(A+B) = dimA + dimB - dim(A intersection B)

3. The attempt at a solution

First of all, dimImT_1 = dimImT_2 = 1 so N_1 = N_2 = n-1.

Also, N_1 + N_2 in V so

dim(N_1 + N_2) = n-1+n-1-dim(N_1 intersection N_2)

<= n and so we get that dim(N_1 intersection N_2) >= n-2.

But since N_1 intersection N_2 in N_1 we get

n-1 >= dim(N_1 intersection N_2) >= n-2. But since N_1 =/= N_2 obviously

dim(N_1 intersection N_2) =/= n-1 and so dim(N_1 intersection N_2) =n-2.

Is that right? Did I leave out any important step?

Thanks.

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

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: Transformations - Kernel

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