(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

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# Column Space problem

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