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!

Kernel, Image

  1. Dec 2, 2014 #1
    1. The problem statement, all variables and given/known data
    Find Kernel, Image, Rank and Nullity of the matrix
    1 −1 1 1 
    | 1 2 −1 1 |
    0 3 -2 0 


    2. Relevant equations


    3. The attempt at a solution
    I have reduced the matrix into rref of
    3 0 1 3
    0 3-2 0
    0 0 0 0
    But am struggling to find the column vectors which are the solutions of that, which I believe is the kernel
    And then I know that the rank and nullity are the dimensions of the image and kernel respectively
     
  2. jcsd
  3. Dec 2, 2014 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The "kernel" of matrix A is the set of all vectors v such that Av= 0. If you write vector v as (a, b, c, d) then any vector in the kernel must satisfy a- b+ c+ d= 0, a+ 2b- c+ d= 0, and 3b- 2c= 0. The "image" is the set of all vectors, v, such that Ax= v for some vector x. If we write vector x as (a, b, c, d) then v must be (x, y, z) such that a- b+ c+ d= x, a+ 2b- c+ d= y, and 3b- 2c= z for some numbers a, b ,c, and d.
     
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: Kernel, Image
  1. Kernels and images (Replies: 2)

  2. Kernel and Image (Replies: 12)

  3. Kernel and image (Replies: 2)

Loading...