A
linear combination of vectors is a
sum of scalar
multiples of those vectors. That is, given a set of

vectors

of the same type,
5.4 such as

(they must have the
same number of elements so they can be added), a linear combination is
formed by multiplying each vector by a
scalar 
and summing
to produce a new vector

of the same type:

For example, let

,

,

, and

. Then the linear combination of

and

is
given by
In
signal processing, we think of a linear combination as a
signal mix. Thus, the output of a
mixing console
may be regarded as a
linear combination of the input signal
tracks.
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