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What is wrong with my matrix inversion?

  1. May 7, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the inverse of the matrix:

    1 1 -1
    2 -1 1
    1 1 2

    2. Relevant equations
    One must be aware of the identity matrix, as well as how add one row to another with matrix multiplication, for example, the matrix

    1 0 0
    k 1 0
    0 0 1

    would add k times the first row to the second row.

    3. The attempt at a solution

    xFZKqU9.jpg

    Which must be wrong, sadly enough.
     
  2. jcsd
  3. May 7, 2015 #2

    Fredrik

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    Staff Emeritus
    Science Advisor
    Gold Member

    After adding -5/2 times the third to the second (step 5), the number in the middle should be 1-5/2, but you wrote -3/5.
     
  4. May 7, 2015 #3

    Mark44

    Staff: Mentor

    You're not doing it the way I learned to do this. How I learned was to set up an augmented matrix with the matrix to invert on the left, and the identity matrix on the right, like so:
    $$\begin{bmatrix} 1 &1 & -1 &| & 1 & 0 & 0\\
    2 & -1 & 1 & | & 0 & 1 & 0\\
    1 & 1 & 2 & | & 0 & 0 & 1 \end{bmatrix}$$
    Now completely row-reduce the matrix on the left to get it to the identity matrix, and your inverse will be on the right. When I did it, there were no "half" entries. Most of the entries had denominators of 3.
     
  5. May 7, 2015 #4
    First of is this the method you learned in class? Because this seems prone to errors.
    You could try Gauss-Jordan Elimination it is essentially the same, but you have some "book keeping" abilities.

    It is similar to Gaussian Elimination for systems of linear equations.

    [Edit] Too late :)
     
  6. May 8, 2015 #5
    Just search for simple linear combinations.
    Math is about using your brains.
    If your method does not work invent a better one or study.
     
  7. May 8, 2015 #6

    SammyS

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    It's true that OP would have benefited from using some simpler combinations.

    However, the method works perfectly well. Fredrik has pointed out where a computational error occurred and Mark has suggest a method with easier "book keeping".
     
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