Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear Algebra problem

  1. Feb 20, 2008 #1
    The problem is prove that for every square singular matrix A there is a nonzero matrix B, such that AB equals the zero matrix.

    I got AB to equal the idenity matrix, but have no clue how to get it to the zero matrix.
     
  2. jcsd
  3. Feb 20, 2008 #2
    If A is viewed as the matrix of a linear transformation, then it being singular is the same as saying that it maps a subspace in the domain to the 0 subspace of the range. Find the kernel of A and let B be a matrix of vectors in that space.
     
  4. Feb 21, 2008 #3
    you said:
    I got AB to equal the idenity matrix, but have no clue how to get it to the zero matrix.

    how did you do that? If A is singular then it doesn't have an inverse, but you found one namely B.
     
  5. Feb 21, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    If A is singular, det(A)= 0. Also det(AB)= det(A)det(B). You, apparently, have proved that det(AB)= 0(det(B)= 0= det(I)= 1. A miracle indeed!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Linear Algebra problem
  1. Linear Algebra Problem (Replies: 2)

  2. Linear algebra problem (Replies: 1)

Loading...