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Homework Help: Matrix Reduction

  1. Mar 15, 2012 #1
    Hi everyone!

    I'm in need for some help with Matrix Reduction! I have two questions:

    Question 1
    Find the inverse of Matrix A by reducing the array (A|I), where
    2 4 6
    4 5 5
    3 1 -3

    Question 2
    Find all solutions of the following system:
    2x1 + 4x2 + x3 - 3x4 - 3x5 = -5
    x1 + 2x2 - x3 + 3x4 - 3x5 = -4
    -2x3 + 7x4 - x5 = 0
    x1 + 2x2 + x4 - x5 = -1

    The first two images are my attempt at question 1 - I get stuck and can't seem to get the identity matrix on the left. I know the answer (in red) through using a Matrix Calculator.

    The last two images are my attempt at question two. I get stuck trying to find x2 and x1 using back substitution. Any suggestions?

    *My apologies for the bad handwriting! Imgur is playing up and won't let me rotate the last 3 photos either :(
    Image 1 - http://imgur.com/hXHhh
    Image 2 - http://tinypic.com/view.php?pic=29kpg5l&s=7
    Image 3 - http://tinypic.com/view.php?pic=9zrkex&s=7
    Image 4 - http://tinypic.com/view.php?pic=33cxfuh&s=7

    Thanks for any help in advanced!
    Last edited: Mar 15, 2012
  2. jcsd
  3. Mar 15, 2012 #2
    Bump! Need help asap!
  4. Mar 15, 2012 #3


    Staff: Mentor

    For the 2nd one, you are going to have one free variable, so let x2 = t. Solve for x1 from that equation. With one free variable, the solution set is not a single point - it's all points on some line in R5.

    When you're done, check that your solution satisfies the original system of equations. If so, then you're done.

    I didn't look at the 1st problem very closely, but at this level of mathematics you should pretty much never write a fraction as a mixed number. For example, 5/3 is good but 1 2/3 is not good - it makes any further calculations more difficult.
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