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

Well the same as the subject..

(a,b,c) is a Basis of [tex]R^{3}[/tex]

does (a+b , b+c , c+a) Basis to [tex]R^{3}[/tex]

I have another question ..

is (a-b , b-c , c-a) Basis to [tex]R^{3}[/tex]

This is know is not true because if I use e1, e2 , e3 I got a error line.

2. Relevant equations

start of liner algebra one.

3. The attempt at a solution

I assume that this is true..

I think something like that.. Because (a,b,c)_ base of [tex]R^{3}[/tex] its means that I can get to a step matrix (Row echelon form)

and the same with (b,c,a) and then I can just add them and get to any soultion that I want... But maybe I'm wrong?

Thank you.

P.S

Can I write base instead of Basis ?

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# Homework Help: If (a,b,c) is a Basis of R3 , Does (a+b,b+c,c+a) also a Basis of R3

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