# Gaussian Elimination - System of Linear Equation

• May 16th 2010, 10:32 PM
mikel03
Gaussian Elimination - System of Linear Equation
Hello everyone,

im having trouble with the following topic i just cant understand what im meant to do.

2x1 + x2 + 2x3 = 4
-2x1 + 2x2 - x3 = 2
-1x + 3x2 + 2x3 = 6

Ive uploaded the question from my revision as jpeg image

if you could help me i need to understand how to complete the question for my exam in two weeks just brain dead when it comes to this topic.

thanks again guys
• May 17th 2010, 02:43 PM
dwsmith
Quote:

Originally Posted by mikel03
Hello everyone,

im having trouble with the following topic i just cant understand what im meant to do.

2x1 + x2 + 2x3 = 4
-2x1 + 2x2 - x3 = 2
-1x + 3x2 + 2x3 = 6

Ive uploaded the question from my revision as jpeg image

if you could help me i need to understand how to complete the question for my exam in two weeks just brain dead when it comes to this topic.

thanks again guys

Your goal is to obtain 1s in the pivot position by addition, multiplication, or multiplying a row and then adding/subtracting it to another.

Step 1: obtain 1 in the $\displaystyle a_{11}$ position.
Step 2: obtain 0s in $\displaystyle a_{21}, a_{31}$ position.
Step 3: obtain 1 in the $\displaystyle a_{22}$ position.
Step 4: obtain 0 in $\displaystyle a_{32}$ position.
Step 5: obtain 1 in the $\displaystyle a_{33}$ position.
• May 17th 2010, 08:34 PM
mikel03
Hello dwsmith,

i still dont understand the method to produce the final answer its in impossible for me.

if possilbe could you work it out for me so i can see how to do it. i just have no idea i came across this topic last year and i understood it but its back again and i have no idea again lol
• May 18th 2010, 04:59 AM
dwsmith
Quote:

Originally Posted by mikel03
Hello dwsmith,

i still dont understand the method to produce the final answer its in impossible for me.

if possilbe could you work it out for me so i can see how to do it. i just have no idea i came across this topic last year and i understood it but its back again and i have no idea again lol

Put in a matrix:
$\displaystyle \begin{bmatrix} a_{11} & a_{12} & a_{13} & :4\\ a_{21} & a_{22} & a_{23} & :2\\ a_{31} & a_{32} & a_{33} & :6 \end{bmatrix}\rightarrow\begin{bmatrix} 2 & 1 & 2 & :4\\ -2 & 2 & -1 & :2\\ -1 & 3 & 2 & :6 \end{bmatrix}$

What should we do first to obtain a 1 in the $\displaystyle a_{11}$ position?