1. Not finding help here? Sign up for a free 30min 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!

Range in Linear Transformation

  1. Apr 11, 2013 #1
    1. The problem statement, all variables and given/known data
    L: R^3 -> R^2
    L(x)=(0,0)^T
    What is the basis, and dim of the Range?


    2. Relevant equations
    Rank(A)-Nullity(A)=n


    3. The attempt at a solution
    So clearly L(x)= (0,0)^T. So the basis must be the empty space and dim is zero, right?

    Now, going of this same logic, Say L(x)=(x2,x3)^T. The basis would be {(1,0)^T, (0,1)^T} does this mean the range is just the Span of these two linearly independent vectors--> Span (v1,v2)?
     
  2. jcsd
  3. Apr 11, 2013 #2

    Mark44

    Staff: Mentor

    Every vector space must consist of at least the zero vector, so a basis for the range of L would be <0, 0>. The dimension of the range is zero, which is what you said.
    That's what a basis is - a set of vectors that spans some space or subspace. In this example, the range is all of R2.
     
  4. Apr 11, 2013 #3
    #44, for the win. Thanks you.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Range in Linear Transformation
Loading...