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Answer:
This is a linearly independent set.
Step-by-step explanation:
We have these following vectors:
In a set of 3 vectors, if one of these vectors can be written as a linear combination of the 2 other vectors, they are linearly dependent. Otherwise, they are linearly independent.
We can verify this by solving the following system:
If the only solution is , they are L.I. Otherwise, they are L.D.
Solution:
We have the following system of equations:
I am going to solve this by the row-reduction of the augmented matrix.
This system has the following augmented matrix:
To reduce the first row, i am going to make these following operations:
So the augmented matrix now is:
Now I reduce the second row, doing:
So the matrix is:
Now we can solve the system:
From the third line, we have that
From the second line:
From the first line
The only solution for this system is . This means that we have a linearly independent set.