In this page linear dependence rank method 4 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 4:
Test whether the vectors (1,1,1), (1,0,1) and (0,2,0) are linearly dependent.
Solution:
linear dependence rank method 4 


R₂ => R₂  R₁ 
1 0 1 1 1 1 () () () _______________ 0 1 0 _______________ 

R₂ => R₂  R₁ 
R₃ => R₃ + 2R₂ 
0 2 0 0 2 0 _______________ 0 0 0 _______________ 
linear dependence rank method 4 linear dependence rank method 4 

R₂ => 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.
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