Matrix Reduction

ivanyo

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!

ivanyo

Bump! Need help asap!

Mark44

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.