Finding a Basis for Subspace in R^4: Linear Algebra Tips

[xsqueetzzz]

Help! Find a basis.
Find a basis for the subspace of R^4 spanned by, S={(6,-3,6,340, (3,-2,3,19), (8,3,-9,6), (-2,0,6,-5)

Figured I would set up the linear combination to test for independence.

 

[Pen_to_Paper]

Do you know how to set up these four vectors as columns to make a 4x4 matrix?

Have you done row reducing?

Because that would also be an approach to determining if they are linearly independent.

 

[xsqueetzzz]

I made up the columns, solved for rref, and came up with the trivial solution

 

[Pen_to_Paper]

As long as you got it to RREF, then you can see if there is a pivot in each column, if there is, then these vectors span R4. If there is not a pivot in each, then they do not span R4.

Good luck!

 

[Mamooie312]

If the determinant of the matrix these vectors make is 0 then some of them are linearly dependent.