Question

Is this set a basis to R3?

[1] [3] [0]
[2] [2] [0]
[3] [1] [1]

What method is used?
Thank You

Answer 1

For vectors to belong to the set of basis
1. they should be linearly independent
2. They should span the space R3.

Answer 2

Okay, would proving the determinant is non-zero be sufficient?

Answer 3

That would probably prove that they are linearly independent right?
you will have to show that for any point (a,b,c) in R3 (a,b,c) = k1v1+k2v2+k3v3

Answer 4

in addition.

Answer 5

Yes i see. Linear independence would be proved. After making Linear combinations would i then sub in a=0, b=0 and c=0 to see if k1=k2=k3=0?

Answer 6

yess.