Who is asking: Student
Level: Secondary
Question:
I am trying to augment a matrix so that i can find the values of the variables
a, b, and c. For the life of me i can't find a solution to the
matrix:
3 -5 2 ' 22
2 3 -1 ' -9
4 3 3 ' 1
I thank you for your help,
Michelle
Hi Michelle,
Multiply the second row by -1 and add it to the third row.
| 3 | -5 | 2 | 22 |
| 2 | 3 | -1 | -9 |
| 2 | 0 | 4 | 10 |
Divide the third row by 2.
| 3 | -5 | 2 | 22 |
| 2 | 3 | -1 | -9 |
| 1 | 0 | 2 | 5 |
Multiply the third row by -2 and add it to the second row.
| 3 | -5 | 2 |
22 |
| 0 | 3 | -5 | -19 |
| 1 | 0 | 2 |
5 |
Multiply the third row by -3 and add it to the first row.
| 0 | -5 | -4 |
7 |
| 0 | 3 | -5 | -19 |
| 1 | 0 | 2 |
5 |
Multiply the second row by 2 and add it to the first row.
| 0 | 1 | -14 |
-31 |
| 0 | 3 | -5 | -19 |
| 1 | 0 | 2 |
5 |
Multiply the first row by -3 and add it to the second row.
| 0 | 1 | -14 |
-31 |
| 0 | 0 | 37 | 72 |
| 1 | 0 | 2 |
5 |
I can't avoid fractions any longer. Divide the second
row by 37.
| 0 | 1 | -14 |
-31 |
| 0 | 0 | 1 |
72/37 |
| 1 | 0 | 2 |
5 |
Finally multiply the second row by 14 and add it to the first row and then multiply the second row by -2 and add it to the third row.
Penny