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Finding kernel of matrix transformation

  1. Oct 9, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the kernel of the matrix transformation given by f(x) = Ax, where

    A =
    1 -1 0
    0 1 -2

    (it's a matrix)

    2. Relevant equations
    Kernel is the set x in R^n for f(x) = Ax = 0

    3. The attempt at a solution
    I set up the problem like this:

    X2 * A = 0

    Just multiplying the matrices I get:

    X1 - X2 = 0
    X2 - 2X3 = 0

    I think I'm missing something really simple but I'm stuck on what to do now in solving the system of equations for X1, X2, X3. Any hints, suggestions, or corrections? thanks
  2. jcsd
  3. Oct 9, 2008 #2


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    Homework Helper

    You have that system of homogenous linear equations. Now represent in a form of a matrix and reduce it to its reduced row echelon form. Then you can read off the values of x1,x2,x3. Denote variables by parameters if you have to.
  4. Oct 9, 2008 #3


    User Avatar
    Homework Helper
    Gold Member

    You have two equations and three unknowns, so you are going to have at least one free parameter, you may as well pick X3=t for your parameter and solve for X1 and X2 in terms of t.
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