Is [3, -8, 1], [6, 2, -5] a Basis for R3?

[fk378]

Homework Statement

Determine whether the set is a basis for R3.

[3, -8, 1] , [6, 2, -5]

The Attempt at a Solution

I know it does not span R3, but the book says it is a basis for a plane in R3. How is it a plane?

 

[steelphantom]

It doesn't span R³, but it does span R², which you can think of as a plane in R³.

 

[Defennder]

You first have to prove that the 2 vectors are linearly independent. To do that, recall the definition of linear dependence for 2 vectors. What does it mean for 2 vectors to be linearly dependent? If it doesn't satisfy that definition, and if none of the vectors is the zero vector, then you would have 2 linearly independent vectors.

If you have only 1 linearly independent vector, then the linear span of that vector would be a line.

The linear span of 2 linearly independent vectors is a plane in R^n.