Solve the system:

x_{1} + 2x_{2} - x_{3} = 1

2x_{1} - x_{2} + x_{3} = 3

-x + 2x_{2} + 3x_{3} = 7

two times the first row subtracted from the second row

1 2 **-2** 1

0 **5** **-5** **-1**

-1 2 3 **3**

Hello frctl. The elements highlighted in red above are not correct.

That first row operation (R2 -> -2*R1 + R2) changes elements in row2

**only**. Why did you change elements in row1 and row3?

Can you post a picture of your paperwork? I would like to see how you organize your work, when doing matrix arithmetic (row operations).

Here's one way to organize the arithmetic for adding -2 times row1 to row2. First, write row1. Next, proofread what you wrote (i.e., confirm that you copied each number correctly). Next, multiply each number by -2, and then double-check that arithmetic. After you've confirmed that -2*R1 is correct, write row2 underneath it. Now proofread, to confirm that you copied each number correctly. Lastly, add those two rows, and then double-check your arithmetic. Written out, the steps would look similar to this:

Code:

```
R2 -> -2*R1 + R2
R1 1 2 -1 1
-----------------------------------
-2*R1 -2 -4 2 -2
+ R2 2 -1 1 3
-----------------------------------
R2 -> 0 -5 3 1
```

Organizing work like that (or something similar) helps to reduce errors because it makes mistakes easier to see (both as you go and when revisiting work later).