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Homework Help: Linear Algebra kernal problem

  1. Nov 19, 2007 #1
    1. The problem statement, all variables and given/known data

    Let T (element of L(R^2,R^2) ) be the linear map T(a,b) = (a+b, 2a +2b)

    A) What is the kernal of T

    B) What is the image of T

    C) Give the matrix for T in the standard basis for R^2

    2. Relevant equations

    Kernal of T = {v element of V st T(v) = 0}
    Image of T = {w element of W st T(v) = w}

    I'm not sure about the matrix


    3. The attempt at a solution

    I'm really not sure where to go with this. In this case, there are two variable (a,b) instead of 1 variable (v), so I don't know how either the kernal or the image work.

    I don't know what standard basis means, and I can't find it in my notes.

    Can someone help me?
     
  2. jcsd
  3. Nov 20, 2007 #2
    Well T is an element of the dual space and it is a map. you want to find the set of points (a,b) such that T(a,b) = (0,0)

    As for the image of T try to visualise what the ap is doing to R2

    The standard basis is what we normally use as a set of basis vectors, which ill leave you to find out (its pretty obvious youll get it)
     
  4. Nov 20, 2007 #3
    The key for the standard basis is R^2. It's different for all R^n, so focus on the two
     
    Last edited: Nov 20, 2007
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