# 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)}

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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

#### 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!!!