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Linear Algebra Matrix with Elementary Row Operations

  1. Sep 25, 2011 #1
    1. The problem statement, all variables and given/known data

    The 3x3 matrix A is transformed into I by the following elementary row operations
    R1+2R3 -> R1
    R2+2R3 ->R2
    2R2 ->R2
    R1 <->R2
    2R3 ->R3

    Find det(A)

    2. Relevant equations

    I assumed to start off with the problem since I was going backwards from I to A. I would do the opposite of each row operation ie
    2R3-R1 ->R1
    2R3-R2 ->R2
    (1/2)R2 ->R2
    R1 <->R2
    (1/2)R3 ->R3

    3. The attempt at a solution

    By finding the det(A) I got -1/4. I'm confused on if I messed up on the row operations. When I did this problem without using the backwards row operations I got -4 which was also wrong. I'd appreciate any help

  2. jcsd
  3. Sep 25, 2011 #2


    Staff: Mentor

    Of the three elementary row operations, only one of them changes the value of the determinant of the matrix. Do you know which one this is?

    Since you end up with the identity matrix (det(I) = 1), you can pick out the row operations that affect the determinant, to get the determinant of your starting matrix.
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