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omeli [17]
3 years ago
8

OF

Mathematics
1 answer:
Kisachek [45]3 years ago
6 0

Answer:

Step-by-step explanation:

A car is rented for $40 per day plus $0.25 per mile driven. The total is $45.50-  40 + 0.25x + 45.50

Karen buys four t-shirts for $45.50. The three red t-shirts each cost 4 times the price of one blue t-shirt.- x + 3(4x) = 45.50

Finn buys a toy boat for $45.50 including tax He was charged 7% sales tax on the original price.- X+0.07% = 45.50

Nick buys a sweater and a jacket for $45.50. The jacket costs 4 times as much as the sweater- 1 X + 4x = 45.50

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Since {v1,...,vp} is linearly dependent, there exist scalars a1,...,ap, with not all of them being 0 such that a1v1+a2v2+...+apvp = 0. Using the linearity of T we have that

a1*T(v1)+a2*T(v1) + ... + ap*T(vp) = T(a1v19+T(a2v2)+...+T(avp) = T(a1v1+a2v2+...+apvp) = T(0) = 0.

Since at least one ai is different from 0, we obtain a non trivial linear combination that eliminates T(v1) , ..., T(vp). That proves that {T(v1) , ..., T(vp)} is a linearly dependent set of W.

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