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

[tex]V=R^{4}\ and\ a^{\rightarrow}, b^{\rightarrow}, c^{\rightarrow}, d^{\rightarrow}, e^{\rightarrow} \in V. [/tex]

(I'll drop the vector signs for easier typing...)

[tex]a = (2,0,3,0), b = (2,1,0,0), c = (-2,0,3,0), d = (1,1,-2,-2), e = (3,1,-5,-2) [/tex]

[tex]Let\ U \subseteq V be\ spanned\ by\ a\ and\ b.\ Let\ W \subseteq V\ be\ spanned\ by\ c,d,e[/tex]

[tex]Compute\ dim_{F}U, dim_{F}W, dim_{F}(U \cap W)[/tex]

2. The attempt at a solution

I guess start with the dimension. We know the vectors a and b span U and by inspection they are linearly independent. Now I'm confused, is the dimension 3 or 4? I think 4 because the vectors have four 'slots' but I also think 3 since the last 'slot' is zero for both.

Also, for [tex]U \cap W[/tex] I would have to prove that a,b,c,d,e are linearly independent before I can find the dimension, no?

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# Homework Help: Dimension of a vector space

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