YAMT: Linear Algebra question

[Syringer]

"Let F be the field of two elements {0,1} where 1+1 = 0. Explicitly write down all elements in F^2 and give a nonempty subset of F^2 that is not a subspace."

I've been staring at this problem for a while now, and just don't understand it. Aren't all the elements just 0, and 1? What is it asking exactly?

 

[TuxDave]

Originally posted by: Syringer
"Let F be the field of two elements {0,1} where 1+1 = 0. Explicitly write down all elements in F^2 and give a nonempty subset of F^2 that is not a subspace."

I've been staring at this problem for a while now, and just don't understand it. Aren't all the elements just 0, and 1? What is it asking exactly?

1+1=0.... 0+0=0..... 1+0=??? *brain explodes*

 

[raptor13]

Isn't it a simple one? F^2 is just [0,0,1,1]. A subset of F^2 would be [1,1] (call it S) and, since it's commonly held that 1+1=2 and not 0, F^2 is not a proper subset of F because the addition rule for F does not hold in S.

Good?

 

[amdskip]

I dunno but I do know my linear algebra teacher sucked and I'm glad I dropped the class. He retired now so I'll have to retake it next semester.

 

[MAME]

Originally posted by: TuxDave

Originally posted by: Syringer
"Let F be the field of two elements {0,1} where 1+1 = 0. Explicitly write down all elements in F^2 and give a nonempty subset of F^2 that is not a subspace."

I've been staring at this problem for a while now, and just don't understand it. Aren't all the elements just 0, and 1? What is it asking exactly?

1+1=0.... 0+0=0..... 1+0=??? *brain explodes*

lol, god I hope you never try binary

 

[helpme]

Linear Algebra sucks. I took it when I didn't have to, and that was a mistake.

 

[Muzzan]

Does F^2 mean the cartesian product F * F? If so, F^2 = { (0, 0), (0, 1), (1, 0), (1, 1) }. However, I don't know how much sense that makes considering the questions asked about F^2 and the info you're given...