Vector Spaces: A Comparison of Two Bases in V3(R)

[ashnicholls]

Are these two sets:

A = {(0,2,2)^T, (1,0,1)^T, (1,2,1)^T}

B= {(1,2,0)^T, (2,0,1)^T, (2,2,0)^T}

Bases of V3(R)

I have found equations that show that they span V3(R)

And that both set are linearly independent.

So am I right in saying that they are both bases of V3(R).

Cheers Ash

 

[matt grime]

If you have three vectors in R^3 that span, then they must be linearly independent, and if you have three linearly independent vectors in R^3 then they must span. That follows from the definition of span and basis.