SOLUTION: Determine which of the following maps f are linear: 1. f : R 3 → R2 2 defined by f(x, y, z) = (x, z)

Algebra ->  College  -> Linear Algebra -> SOLUTION: Determine which of the following maps f are linear: 1. f : R 3 → R2 2 defined by f(x, y, z) = (x, z)      Log On


   

Question 1203447: Determine which of the following maps f are linear:
1. f : R
3 → R2
2 defined by f(x, y, z) = (x, z)
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

This writing/printing is terrible, and it requires some mind efforts to decipher.


        If it is   f: R%5E3 ---> R%5E2   defined as   f(x,y,z) = (x,z),

        then it is a projection from   R%5E3   to the plane   (x,z).

        Projection is  ALWAYS  a linear map.