Show that the product is equal to the unit matrix.
Hello, Greg!
Since you are studying Inverses, I assume you know how to multiply.
What's stopping you?
Code:| 1 1 1 | | 3 -3 1 | Prove that: | 1 2 3 | is the inverse of | -3 5 -2 | | 1 3 6 | | 1 -2 1 |. . . . . . . . .↑Code:| 1 1 1 | | 3 -3 1 | | 1 2 3 |.| -3 5 -2 | | 1 3 6 | | 1 -2 1 | | 1(3) + 1(-3) + 1(1) 1(-3) + 1(5) + 1(-2) 1(1) + 1(-2) + 1(1) | = | 1(3) + 2(-3) + 3(1) 1(-3) + 2(5) + 3(-2) 1(1) + 2(-2) + 3(1) | | 1(3) + 3(-3) + 6(1) 1(-3) + 3(5) + 6(-2) 1(1) + 3(-2) + 6(1) | | 3 - 3 + 1 -3 + 5 - 2 1 - 2 + 1 | = | 3 - 6 + 3 -3 + 10 - 6 1 - 4 + 3 | | 3 - 9 + 6 -3 + 15 - 12 1 - 6 + 6 | | 1 0 0 | = | 0 1 0 | | 0 0 1 |
Use the slide-bar to see the rest of line 2.
Edit: corrected the typo!
I disagree.
| 1 0 1 |
| 0 1 0 |
| 0 0 1 |
Is not the identity matrix. A way to check this would be to augment the original Matrix with it's identity matrix and row reduce it to see what the inverse is.
That is, in this case,
M := Matrix([[3, -3, 1, 1, 0, 0], [-3, 5, -2, 0, 1, 0], [1, -2, 1, 0, 0, -1]])
(Using Maple notation). In which case, once that is row reduced, you get:
Matrix([[1, 0, 0, 1, 1, -1], [0, 1, 0, 1, 2, -3], [0, 0, 1, 1, 3, -6]])
The ABOVE matrix is the inverse matrix (in augmented columns), that is:
Matrix([[1, 1, -1], [1, 2, -3], [1, 3, -6]])