1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Linear Mappings Question

  1. Jan 11, 2010 #1
    1. The problem statement, all variables and given/known data

    http://img526.imageshack.us/img526/743/93134049.png [Broken]

    2. Relevant equations
    Just the standard linear mapping properties and theorums.

    3. The attempt at a solution

    I have already solved part A by considering the transformation A: Rn -> R | A(x) = a.x where x is a vector in Rn, and finding the dimension of the nullspace.

    I am stuck on where to begin the proof for part b, once I have b I don't think I will have a problem generalizing it for part c.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jan 11, 2010 #2
    Your solution to part (a) already contains the essence of a solution to part (b); just think about the dimension of the null space of a different linear map [tex]B[/tex], one that uses the existence of [tex]\vec{a}[/tex] and [tex]\vec{b}[/tex] both.

    (If you need a further hint: given that you are supposed to find that [tex]\dim(S \cap T) = n - 2[/tex] in case [tex]\vec{a}[/tex] and [tex]\vec{b}[/tex] are linearly independent, what do you think the dimension of the range space of [tex]B[/tex] ought to be?)
  4. Jan 11, 2010 #3
    ah, thank you, very good. I have a transformation B: Rn -> R2 that works nicely, and the generalization follows quite easily.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook