ME – 210
Applied Mathematics for Mechanical Engineers
Prof. Dr. Faruk Arınç
Spring 2010
Linear Dependence and Independence of Vectors
Given any set of m vectors [x
1
], [x
2
], … , [x
m
] with the same number of components
in each, and any set of m scalars c
1
, c
2
, … , c
m
,
if the
linear combination
of these vectors is a
null vector
¸ i.e.,
c
1
[x
1
] + c
2
[x
2
] + … + c
m
[x
m
]
=
[0]
only when
c
1
= c
2
= … = c
m
= 0
then, [x
1
], [x
2
], … , [x
m
]
are said to be
linearly independent
.
If there is at least one non–zero c
i
for which the condition is valid, then these vectors
are said to be
linearly dependent
.

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