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Elementary row operations- Linear Algebra

  1. Sep 16, 2011 #1
    1. The problem statement, all variables and given/known data

    Consider the following 3 row operations performed to a 4x3 matrix A used to transform it into matrix B:
    E1: -4R1+R4-> R4
    E2: R2<->R3
    E3: (1/2)R4-> R4
    From there I am asked to find E1, E2, E3.

    3. The attempt at a solution

    I assumed the identity matrix I would start out with was
    1 0 0
    0 1 0
    0 0 1
    0 0 0

    and then by using E1 the matrix would become
    1 0 0
    0 1 0
    0 0 1
    -4 0 0

    However, the answer was counted wrong. Am I approaching the question the wrong way or am I using the wrong identity matrix?
     
  2. jcsd
  3. Sep 16, 2011 #2
    The identity matrix is actually 4x4:
    [1 0 0 0
    0 1 0 0
    0 0 1 0
    0 0 0 1]
     
  4. Sep 16, 2011 #3
    ohh thank you so much! I got the correct answers but why is the identity matrix a 4x4 when the original matrix is a 4x3?
     
    Last edited: Sep 16, 2011
  5. Sep 16, 2011 #4

    Ray Vickson

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    Science Advisor
    Homework Helper

    Because you perform row operations on an mxn matrix by multiplying on the left by an mxm matrix.

    RGV
     
  6. Sep 16, 2011 #5
    what he said.
     
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