SOLUTION: how do i prove W^(perpendicular sign) is a subspace of R^n

Algebra ->  College  -> Linear Algebra -> SOLUTION: how do i prove W^(perpendicular sign) is a subspace of R^n      Log On


   

Question 29237: how do i prove W^(perpendicular sign) is a subspace of R^n
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
how do i prove W^(perpendicular sign) is a subspace of R^n
WHAT IS THIS W^(perpendicular sign)?PLEASE CLARIFY OR COPY THE PROBLEM AS IT IS.
IN GENERAL TO SHOW THAT W IS A SUB SPACE , WE TAKE 2 ELEMENTS ALPHA AND BETA FROM W AND 2 SCALARS IN REAL FIELD SAY X AND Y AND SHOW THAT
X*ALPHA+Y*BETA IS ALSO AN ELEMENT OF W..WHICH IS NECESSARY AND SUFFICIENT CONDITION FOR W TO BE A SUBSPACE OF R^N