Determine if this is a linearly dependent or independent set: (v, v, v ) where syon v = (1,2,2,-1), v = (4,9,9,-4), v = (5,8,9,-5). show all work and explain your reasoning carefully

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.