The rule I(p) = 400p - 20p^2 can be used to estimate the income (I) from ticket sales on based on the ticket price (p)
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Not necessarily. 
and 
may be linearly dependent, so that their span forms a subspace of 
that does not contain every vector in .
For example, we could have
and 
. Any vector 
of the form 
, where 
, is impossible to obtain as a linear combination of these and , since
unless
and 
.
For example, we could have
unless