List 5 vectors in Span $v1,v2$. For each vector, display the weights on $carolannpeacock.combf v1$ and also $carolannpeacock.combf v2$ supplied to geneprice the vector and list the three entries of the vector. Do not make a sketch.

$$ carolannpeacock.combf v1 = eginbmatrix 3 \0 \2 \ endbmatrix, carolannpeacock.combf v2 = eginbmatrix -2 \0 \3 \ endbmatrix $$

I execute not really understand also what it indicates by weights I assume in can expect multiplication. I think the answer is:

$$v3 =eginbmatrix 1 \0 \5 \ endbmatrix $$ Because I assume that you include them. How does one select their weights?


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I did not understand the term weights in this context, yet it is most likely to expect the multiples $w_i$ of the spanning vectors $v_i$:$$Declarecarolannpeacock.comOperatorspanSpanspanv_1, v_2 = w_1 v_1 + w_2 v_2 mid w_1, w_2 in carolannpeacock.combbR $$

Note: In other contexts, like straight optimization, there could be conditions applied on those weight factors, e.g. $w_i ge 0$ or $sum_i w_i = 1$.

The resulting linear combicountries would certainly have actually one-of-a-kind names, the first would certainly cause conical combinations, all of them developing the conical hull, the second in affine combicountries (affine hull), if both apply it outcomes in convex combicountries (convex hull).

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Choose 5 pairs of scalars, $ a_1, a_2 $, and create the collection of vectors consisting of $a_1 carolannpeacock.combf v1 + a_2 carolannpeacock.combf v2$ utilizing each such pair.


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