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  3. 1. let ? be a finite dimensional vector space with

1. Let ? be a finite dimensional vector space with basis {?1,...,??} and ? ? L(?). Show the...

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Advance Math

1.Let ? be a finite dimensional vector space with basis {?1,...,??}and ? ? L(?).
Show the following are equivalent:
(a) The matrix for ? is upper triangular. (b) ?(??) ?Span(?1,...,??) for all ?.
(c) Span(?1,...,??) is ?-invariant for all ?.

please also explain for (a)->(b) why are all the ccoefficients 0 for all i>k? and why T(vk) in the span of(v1,.....,vk)? i need help understanding this.

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