Let V be a 9 dimensional vector space and let U and W(adsbygoogle = window.adsbygoogle || []).push({});

be five dimensional subspaces of V with the bases Bu

and Bw respectively,

(a) show that if Bu intersect Bw is empty then

Bu union Bw is linearly dependen

(b)use part (a) to prove U intersect W is not

equal to the 0 vector

now i have already done part (a), now i have already

done part (a). can you please help me..

for part a.. this is what i have briefly....

we know Bu intersect Bw has nothing in common.

Since Bu and Bw is a basis we know that it is linearly independent.

Therefore Let bu be a linearly independent

subset of a vector space V and let Bw be a

vector in V that is not in Bu, then Bu union Bw

is linearly dependent iff Bw is in the span of Bu... (by a theorem)

by definition of a basis we know, span ( Bu) = v

therefore, the question now is if Bw is in V

which is true ( definition of a basis)... therefore

Bu union Bw is linearly dependent if Bu intersect Bw is nothing...

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# Homework Help: Linear algebra, subspace

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