Homework SourseFind the determinant of A1 Given A 1 1 5 3 1 0 0 1 2 1 1 0
Find the determinant of A-1.
Given: A =
| 1 | 1 | -5 | 3 |
| 1 | 0 | 0 | 1 |
| 2 | -1 | -1 | 0 |
| 0 | 1 | 0 | 1 |
Solution
Your matrix
Eliminate elements in the 1st column under the 1st element
Eliminate elements in the 2nd column under the 2nd element
Eliminate elements in the 3rd column under the 3rd element
Multiply the main diagonal elements
1 x (-1) x (-6) x (-1) = -6
Result:
Determinant is -6
Find the determinant of A-1 = -1/6 (answer)
| Sign | A1 | A2 | A3 | A4 | |
|---|---|---|---|---|---|
| + | 1 | 1 | 1 | -5 | 3 |
| 2 | 1 | 0 | 0 | 1 | |
| 3 | 2 | -1 | -1 | 0 | |
| 4 | 0 | 1 | 0 | 1 |
