William W. answered • 07/20/21
Top Pre-Calc Tutor
The answer to this question is hard to provide by typing it out. The augmented matrix is:
To find the reduced row form, you want to get it into the form:
where there are "1's" down the diagonal and the final column then is the answers for x, y, and z. To do that, use row operations with the following rules:
1. Any two rows may be interchanged.
2. The elements of any row may be multiplied by a nonzero constant.
3. Any row may be changed by adding each corresponding element of a different row to it.
For instance, to get started you may choose to multiply row 1 by "-2" then add it to row 2, the results of which would be placed in row 2 as the "new row 2". Multiplying row 1 by "-2" gives -2 -6 -2 | 0 and adding this to row 2 results in the following:
--- ---
| 1 3 1 | 0 |
| 0 -5 -1 | 15 |
| 1 2 5 | 27 |
--- ---
Then we could divide row 2 by -5 and put the results in as the new row 2:
--- ---
| 1 3 1 | 0 |
| 0 1 1/5 | -3 |
| 1 2 5 | 27 |
--- ---
Perhaps then you multiply row 1 by -1 and add the results to row 3, replacing row 3 with those results which gives:
--- ---
| 1 3 1 | 0 |
| 0 1 1/5 | -3 |
| 0 -1 4 | 27 |
--- ---
Then perhaps add row 2 to row 3 and put the results in as the new row 3:
--- ---
| 1 3 1 | 0 |
| 0 1 1/5 | -3 |
| 0 0 21/5 | 24 |
--- ---
Now, multiply row 3 by 5/21 to get:
--- ---
| 1 3 1 | 0 |
| 0 1 1/5 | -3 |
| 0 0 1 | 40/7 |
--- ---
Then perhaps multiply row 3 by -1/5 and add it to row 2 and replace row 2 with the results. Etc, etc
The bottom line is that, when you get all the left side as all zeros except the diagonal as "1's" then the right column gives you the answers. You should get x = 47/7, y = -29/7, and z = 40/7
