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

Obtain the column space of the following matrix

B = 2 -3 -1

2 -3 -1

-3 3 2

2. Relevant equations

Linear independence test

c1V1 + c2V2 + ...... + cnVn = 0

c1=c2=...cn=0

3. The attempt at a solution

Please see attachment

I cannot get the answer which is CS(B) = span{ (2,2,-3)^T, (1,1,-1)^T } where T denotes transpose

The (1,1,-1)^T can be realised by adding a(2,2,-3)^T and c(-1,-1,2)^T together (where a=c) and setting a=1

but the problem is that it destroys the linear independence of (1,1,-1)^T since it depends on (2,2,-3)^T to generate the result

**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: Column Space problem

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