Row reduction, Gaussian Elimination on augmented matrix

In summary: Yes. You can skip some of the steps for brevity if you are comfortable with this. For example you don't really need to write0*¼ 0*¼ 4*¼ | 8*¼You could immediately write0 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 = -20·x + 1·y - 1·z = -30·x + 0·y +1·z = 2Also
  • #1
Rafa3D
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Member warned to post homework questions in the proper forum section
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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  • #2
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!
 
  • #3
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 :(
 
  • #4
Why don't you start by listing out all the operations you can do.
 
  • #5
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.
 
  • #6
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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  • #7
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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