# Matrix Reduction

by ivanyo
Tags: matrix, reduction
 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 (A|I), where A= 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!
 P: 5 Bump! Need help asap!
 Mentor P: 19,707 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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