Solve the system:
x1 + 2x2 - x3 = 1
2x1 - x2 + x3 = 3
-x + 2x2 + 3x3 = 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).
?
