In this page linear dependence rank method 2 we are going to see some example problem to understand how to test whether the given vectors are linear dependent.
Procedure for Method II
Example 2:
Test whether the vectors (1,3,1), (-1,1,1) and (3,1,-1) are linearly dependent.If so write the relationship for the vectors
Solution:
|
R₂ => R₂ + R₁ |
-1 1 1 1 3 1 ___________________ 0 4 2 __________________ |
linear dependence rank method 2 linear dependence rank method 2 |
R₃ => R₃ - 3R₁ |
3 1 -1 3 9 3 (-) (-) (-) _________________ 0 -8 -4 _________________ |
|
R₂ => R₂ + R₁ R₃ => R₃ - 3R₁ |
R₃ => R₃ + 2R₂ |
0 -8 -4 0 8 4 _______________ 0 0 0 _______________ |
|
R₃ => R₃ + 2R₂ |
Number of non zero rows is 2. So rank of the given matrix = 2.
If number of non zero vectors = number of given vectors,then we can decide that the vectors are linearly independent. Otherwise we can say it is linearly dependent.
Here rank of the given matrix is 2
which is less than the number of given vectors.So that we can decide the
given vectors are linearly dependent. linear dependence2 rank method
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