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Matrix Reduction 
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#1
Mar1512, 12:19 AM

P: 5

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 (AI), where A= 2 4 6 4 5 5 3 1 3 Question 2 Find all solutions of the following system: 2x_{1} + 4x_{2} + x_{3}  3x_{4}  3x_{5} = 5 x_{1} + 2x_{2}  x_{3} + 3x_{4}  3x_{5} = 4 2x_{3} + 7x_{4}  x_{5} = 0 x_{1} + 2x_{2} + x_{4}  x_{5} = 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 x_{2} and x_{1} 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! 


#2
Mar1512, 09:32 AM

P: 5

Bump! Need help asap!



#3
Mar1512, 01:03 PM

Mentor
P: 21,284

For the 2nd one, you are going to have one free variable, so let x_{2} = t. Solve for x_{1} from that equation. With one free variable, the solution set is not a single point  it's all points on some line in R^{5}.
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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