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A simple Linear Algebra question that seems so hard

  1. Mar 25, 2010 #1
    1. The problem statement, all variables and given/known data

    Is the statement true or sometimes false. Justify your answer:

    The determinant of a matrix is unchanged if the columns are written in reverse order.

    2. Relevant equations

    3. The attempt at a solution

    I understand that the only thing that is changed is the sign (negative to positive or visa-versa), but do not understand the proof of how.
  2. jcsd
  3. Mar 25, 2010 #2
    how do you find the determinant of a matrix?
  4. Mar 25, 2010 #3
    One way would be via cofactor expansion.

    I.e. 3x3 matrix determinant =a11C11+a12C12+a13C13
  5. Mar 25, 2010 #4
    okay good. so if you switched the columns, how would the cofactor expansion change?
  6. Mar 25, 2010 #5
    and calculate out those cofactors when you do it.
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