SOLUTION: If {vector u, vector v, vector w} is linearly independent then u, v, and w are not in R^2 (2 space). True or false? and why? Thanks for your help!

Algebra ->  College  -> Linear Algebra -> SOLUTION: If {vector u, vector v, vector w} is linearly independent then u, v, and w are not in R^2 (2 space). True or false? and why? Thanks for your help!      Log On


   

Question 964561: If {vector u, vector v, vector w} is linearly independent then u, v, and w are not in R^2 (2 space). True or false? and why? Thanks for your help!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
True, because if u,v, and w are in R2, then you could write w as a linear combination of u and v, which would make it a linearly dependent system. So u, v, and w cannot be in R2.