Row reduction, Gaussian Elimination on augmented matrix

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Discussion Overview

The discussion revolves around the process of row reduction and Gaussian elimination applied to an augmented matrix. Participants seek guidance on how to manipulate the matrix to achieve specific values in certain positions, particularly focusing on achieving zeros and ones in designated locations.

Discussion Character

  • Homework-related
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant requests assistance in modifying a specific matrix, expressing difficulty in the process.
  • Another participant suggests a step-by-step approach to row reduction, emphasizing the use of the first row to eliminate entries in subsequent rows.
  • A participant expresses confusion about the provided guidance and seeks further clarification.
  • Another participant advises starting by listing all possible row operations to clarify the steps needed.
  • Multiple participants emphasize the importance of demonstrating personal effort before receiving help, suggesting specific questions to answer related to the matrix operations.
  • A later reply indicates an understanding of the process and discusses the possibility of skipping steps for brevity, while also correcting a misunderstanding about labeling rows in the final matrix.

Areas of Agreement / Disagreement

Participants generally agree on the need for a structured approach to row reduction, but there is some confusion regarding the application of the steps and the labeling of rows in the final matrix. The discussion remains unresolved in terms of specific methodologies and interpretations of the steps involved.

Contextual Notes

Some participants highlight the necessity of showing work and understanding the operations involved, while others express uncertainty about the instructions given. There are also mentions of external resources, such as YouTube videos, which may provide additional context.

Rafa3D
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Hi! Please, could you help me on how to solve the following matrix ?
I need to replace the value 3 on the third line by 0, the first column need to remain zero and 1 for the third column. I'm having a lot of difficulties with this. How would you proceed ?

1680987895171.png


Thank you for your time and help.
All best
 
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Usually you go row by row. Use the first row to knock out the first entry of the second row, then the first row to knock out the first entry of the third row, and then the second row to knock out the second entry of the third row. The first two parts are done for you in this matrix!
 
Office_Shredder said:
Usually you go row by row. Use the first row to knock out the first entry of the second row, then the first row to knock out the first entry of the third row, and then the second row to knock out the second entry of the third row. The first two parts are done for you in this matrix!
I m sorry, but I still don't understand :(
 
Why don't you start by listing out all the operations you can do.
 
Hi @Rafa3D. Welcome to PF.

The general rule here is that you have to show evidence of your own effort before we help. You will get guidance/steering/advice rather than answers. That being said…

Let’s use ‘R1’ as shorthand for 'row one' for example.

Q1. What would R2 be if you multiplied it by 3? Tell us what it would be.

Q2. Subtract your answer from R3 (four subtractions to do). You will get a new R3 but R1 and R2 haven’t changed. Tell us what the matrix is now.

If you answer Q1 and Q2 correctly, there’s one final step.

Note, there are many YouTube videos explaining this.
 
Steve4Physics said:
Hi @Rafa3D. Welcome to PF.

The general rule here is that you have to show evidence of your own effort before we help. You will get guidance/steering/advice rather than answers. That being said…

Let’s use ‘R1’ as shorthand for 'row one' for example.

Q1. What would R2 be if you multiplied it by 3? Tell us what it would be.

Q2. Subtract your answer from R3 (four subtractions to do). You will get a new R3 but R1 and R2 haven’t changed. Tell us what the matrix is now.

If you answer Q1 and Q2 correctly, there’s one final step.

Note, there are many YouTube videos explaining this.
Thank you. I think I got the idea :

1681049851166.png
 
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Rafa3D said:
Thank you. I think I got the idea :

View attachment 324667
Yes. You can skip some of the steps for brevity if you are comfortable with this. For example you don't really need to write
0*¼ 0*¼ 4*¼ | 8*¼
You could immediately write
0 0 1 | 2.

And you have labelled the rows of the final matrix as x, y and z on the left side. That's wrong here. Remember your final matrix represents these equations:
1.x + 1·y - 1·z = -2
0·x + 1·y - 1·z = -3
0·x + 0·y +1·z = 2

Also, you are allowed to swap rows, so it makes no sense to label a row as x or y or z.
 

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