Feeling retarded ATM (1 Viewer)

[hayabusaboston]

Havent been following lectures and now don't know what these mean, question 1 the "express as..." part

http://imgur.com/a/HckCP

Can someone just do the first one and I'll understand how to do the rest? I known how to show is or isn't subspace just evoressing as set of vectors idk maybe I'm retarded

 

[hayabusaboston]

Oh and determine if subspace of R^n means the subsists of R^(number of vectors) right??

 

[Test123456]

Hi there,

I'm not sure if you still need help with this as it has been over a month since you asked, but 1a is not closed under scaler multiplication and hence is not a subspace. 1b and c are similarly, not subspaces (I'll leave it to you to figure out why). 1d is a subspace (you can check all 3 defining axioms yourself). To express this as a span of vectors, consider a general vector in R^3, (a,b,c). We know that

a + b + c = 0 ... (1) and
a + b - c = 0 ... (2)

(1)-(2) gives
2c =0 => c = 0

and hence
a + b = 0 => a = -b

We can go back and write our general vector as (-b,b,0) which is the same as span{(-1,1,0)}.