Gaussian Elimination - System of Linear Equation

Mar 2009
21
0
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
 

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dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
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.
 
Mar 2009
21
0
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
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
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?