For the following set of vectors, determine whether it is linearly independent or linearly dependent. If it is linearly dependent, find all its maximum linearly independent subsets? {(1,2,-1),(2,4,6),(0,0,-8)}
from my ERO, I found out that it is linearly dependent but I dont know how to find its linearly independent subsets
from my ERO, I found out that it is linearly dependent but I dont know how to find its linearly independent subsets
1 Answer
Please see the explanation below.
Explanation:
The vectors are
The vectors are independent if
Where
has only the trivial solution
Perform a row reduction on the augmented matrix
Since there is a free variable, the system is not linearly independant
The determinant of the matrix
Therefore,
So,
Hope that this will help!!!