A vector v = (a,..., an) ER is called strongly positive if a; > 0 for...

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A vector v = (a₁,..., an) ER" is called strongly positive if a; > 0 for all i = 1,..., n. a) Suppose that v is strongly positive. Show that any vector that is "close enough" to v is also strongly positive. (Formulate carefully what "close enough" should mean.) b) Prove that if a subspace S of R" contains a strongly positive vector, then S has a basis of strongly positive vectors. A vector v = (a₁,..., an) ER" is called strongly positive if a; > 0 for all i = 1,..., n. a) Suppose that v is strongly positive. Show that any vector that is "close enough" to v is also strongly positive. (Formulate carefully what "close enough" should mean.) b) Prove that if a subspace S of R" contains a strongly positive vector, then S has a basis of strongly positive vectors.

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ANSWER a To show that any vector close enough to a strongly positive vector v is also strongly positive we need to formulate what close enough means O... View the full answer