Let U,W sube V, vector subspaces then: 1) U sube W => W^(_|_) sube U^(_|_) 2) (U+W)^(_|_)=U^(_|_) nn W^(_|_)

Haiphongum 2022-09-16 Answered
Let U , W V, vector subspaces then:
1) U W W U
2) ( U + W ) = U W
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Answers (1)

Julianne Mccoy
Answered 2022-09-17 Author has 10 answers
1)Let v W , which means that ( w W ) : v , w = 0. You want to prove that v U . Take u U. But then u W and therefore v , u = 0. So, v U
2)Since U U + W and V U + W, ( U + W ) U and ( U + W ) W .. Therefore ( U + W ) U W . Now, take v V ( U + W ) . Then there is some u U and there is some w W such that v , u + w 0. Therefore, the numbers v , u and v , w cannoy be both equal to 0. In particular, v U W

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