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Invertible matrix

  1. Nov 4, 2007 #1
    I have to write all possible equivalent conditions to "A is invertible," where A is an nxn matrix. can anyone help me out with this question
  2. jcsd
  3. Nov 4, 2007 #2


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    Name one. You aren't trying very hard.
  4. Nov 4, 2007 #3
    i dont understand the question
  5. Nov 4, 2007 #4


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    well you know that A^-1 = 1/det|A| *adj(A)

    so for this to exist...det|A| can't be zero...and think of row-echelon form when finding A^-1

    in row-echelon form, to get A^-1. how many non-zero rows must it have?How many pivot positions must it have?
  6. Nov 4, 2007 #5


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    Here's another one. A is invertible if there is a matrix B such that A*B=I. You are way behind. How about a statement in terms of the dimension of the kernel? How about expressing invertability in terms of the solutions to a system of linear equations? There's a lot of ways to express this concept.
  7. Nov 4, 2007 #6
    A is also invertible when the determinant does not equal to 0
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