# Statistics Dictionary

To see a definition, select a term from the dropdown text box below. The statistics dictionary will display the definition, plus links to related web pages.

Select term:

### Linear Dependence of Vectors

A set of vectors is linearly independent if no vector in the set is (a) a scalar multiple of another vector in the set or (b) a linear combination of other vectors in the set; conversely, a set of vectors is linearly dependent if any vector in the set is (a) a scalar multiple of another vector in the set or (b) a linear combination of other vectors in the set.

Consider the row vectors below.

a =
 1 2 3
d =
 2 4 6
b =
 4 5 6
e =
 0 1 0
c =
 5 7 9
f =
 0 0 1

Note the following:

• Vectors a and b are linearly independent, because neither vector is a scalar multiple of the other.

• Vectors a and d are linearly dependent, because d is a scalar multiple of a; i.e., d = 2a.

• Vector c is a linear combination of vectors a and b, because c = a + b. Therefore, the set of vectors a, b, and c is linearly dependent.

• Vectors d, e, and f are linearly independent, since no vector in the set can be derived as a scalar multiple or a linear combination of any other vectors in the set.