Homework SourseIf A 1 0 0 0 2 1 0 0 6 2 1 0 8 2 3 1 then A1 SolutionFirst
If A = [1 0 0 0 2 1 0 0 6 2 1 0 -8 2 3 1] then A^-1 =
![If A = [1 0 0 0 2 1 0 0 6 2 1 0 -8 2 3 1] then A^-1 = SolutionFirst, let\'s add the Identity Matrix to the right of our matrix Now, let\'s do Gauss-Jordan Elim](/WebImages/38/if-a-1-0-0-0-2-1-0-0-6-2-1-0-8-2-3-1-then-a1-solutionfirst-1114810-1761591931-0.webp "If A = [1 0 0 0 2 1 0 0 6 2 1 0 -8 2 3 1] then A^-1 = SolutionFirst, let\'s add the Identity Matrix to the right of our matrix Now, let\'s do Gauss-Jordan Elim")
Solution
First, let\'s add the Identity Matrix to the right of our matrix
Now, let\'s do Gauss-Jordan Elimination on our new matrix...
Add (-2 * row1) to row2
Add (-6 * row1) to row3
Add (8 * row1) to row4
Add (-2 * row2) to row3
Add (-2 * row2) to row4
Add (-3 * row3) to row4
The inverse matrix can now be found in the right 4 columns of our reduced row echelon matrix
Here is the inverse matrix:
| 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 2 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
| 6 | 2 | 1 | 0 | 0 | 0 | 1 | 0 |
| -8 | 2 | 3 | 1 | 0 | 0 | 0 | 1 |
