Homework 6 Vectors

Name:

[3pts] Find the dot product of the following:
u=[3 4 5 1], v=[10-12 5 10] ∈R
u=[1 1 1 0 0 1], v=[1 0 1 0 1 1] ∈GF(2)
u=[-10 0 5 6 12 8], v=[1-100 50 6 7 25] ∈R
[3pts] Solve the lights out problem for:
* *
*
*

* *

[4pts] Show that for 2-vectors in GF(2) if the dot product (u∙v)=0 and if u=(u_1,u_2) and v=(v_1,v_2) then u_1*u_2*v_1*v_2=0