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

Suppose V = 2^Ω where Ω = {red,blue,yellow,green}. Verify whetheru={blue,green},v={red,yellow,green}, andw={blue,yellow} are linearly independent in V

3. The attempt at a solution

I let

red = a1

blue = a2

yellow =a3

green = a4

therefore Ω = {a1, a2, a3, a4}

so nowu={a2,a4},v={a1,a3,a4},w={a2,a3}

These vectors can also be written as

u=0.a1+1.a2+0.a3+1.a4

v=1.a1+0.a2+1.a3+1.a4

w=0.a1+1.a2+1.a3+0.a4

writing these vectors out in one matrix gives us

(0 | 1 | 0

1 | 0 | 1

0 | 1 | 1

1 | 1 | 0) if we're supposed to write the vectorsas columns

then i reduced it to REF to get

(1 | 0 | 0

0 | 1 | 0

0 | 0 | 1

0 | 0 | 0)

But then what do I do? How do I know what is dependent or not? I thought I could just say a1=0, a2=0,a3=0,a4=free. That shows these are independent but there is an empty row surely something's dependent??

**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: Linear dependence of non-numerical objects

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

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