- #1
Saladsamurai
- 3,020
- 7
I that this is probably another really simple question, but I would like some help learning how one starts a 'verification problem.'
Verify that Fn is a vector space over F.
I know that I just have to show that commutativity and scalar multiplication etc. are satisfied. But I am not used to approaching problems with such generality.
I am thinking that I should first define the elements of Fn; maybe like:
Fn={(x1,...,xn) : xj [itex]\epsilon[/itex] F for j=1,2,...,n}.
Now what? This seems kind of redundant... for commutativity I would just show that
[tex](x_1,x_2,x_3,...,x_n)+(y_1,y_2,y_3,...,y_n)=(x_1+y_1,x_2+y_2,x_3+y_3,...x_n+y_n)=(y_1+x_1,y_2+x_2,y_3+x_3,...,y_n+x_n)[/tex]
Right? Is this the right approach?
Verify that Fn is a vector space over F.
I know that I just have to show that commutativity and scalar multiplication etc. are satisfied. But I am not used to approaching problems with such generality.
I am thinking that I should first define the elements of Fn; maybe like:
Fn={(x1,...,xn) : xj [itex]\epsilon[/itex] F for j=1,2,...,n}.
Now what? This seems kind of redundant... for commutativity I would just show that
[tex](x_1,x_2,x_3,...,x_n)+(y_1,y_2,y_3,...,y_n)=(x_1+y_1,x_2+y_2,x_3+y_3,...x_n+y_n)=(y_1+x_1,y_2+x_2,y_3+x_3,...,y_n+x_n)[/tex]
Right? Is this the right approach?
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