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Geometric Transformations
Scalar Multiplication--2
Linear Dependence
Set of all scalar multiples of a vector is a line through the origin
Two vectors are linearly dependent when one is a multiple of the other
Definition of dependence for three or more vectors is trickier
Basis vectors of the plane
The unit vectors (i.e., whose length is one) on the x and y-axes are called the standard basis vectors of the plane
The collection of all scalar multiples of 
gives the first coordinate axis, and
The collection of all scalar multiples of 
gives the second coordinate axis
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Geometric Transformations - 09 MAY 95
Page 16 of 51
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