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Kernels and images

  1. Feb 22, 2007 #1
    1. The problem statement, all variables and given/known data
    Consider a matrix A, and let B = rref(A)
    (a) Is ker(A) necessarily equal to ker(B)? Explain.
    (b) Is im(A) necessarily equal to im(B)? Explain.

    2. Relevant equations

    3. The attempt at a solution
    I feel confident saying yes for (a) and no for (b), and what I can articulate is that (a) is true because the kernel is the augmented matrix with the last column with all zeros, thus, it is irrelevant whether or not the matrix is in rref. But I don't know how to express (b).
  2. jcsd
  3. Feb 22, 2007 #2


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    Staff Emeritus
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    What does rref mean?
  4. Feb 22, 2007 #3
    It's reduced row-echelon form, but nevermind, I got the answer, though thanks for the help.
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