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Invertible matrix

  • Thread starter eyehategod
  • Start date
  • #1
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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
 

Answers and Replies

  • #2
Dick
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Name one. You aren't trying very hard.
 
  • #3
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i dont understand the question
 
  • #4
rock.freak667
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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?
 
  • #5
Dick
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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.
 
  • #6
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A is also invertible when the determinant does not equal to 0
 

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