anonymous 5 years ago Can someone please explain me how to inverse a matrix?

1. anonymous

Comin up......

2. anonymous

|dw:1326942286656:dw|

3. anonymous

There is a systematic way to find the inverse of a matrix that isn't so difficult. It might take a bit to type up, so bear with me!

4. anonymous

LOL Thanks :D My book doesn't show how it got it so I am just wondering how

5. anonymous

I think u gotta use G-J elimination

6. anonymous

i think you need the determinant with it also

7. anonymous

but only if it is 2by 2 matrix no?

8. anonymous

First, you create a 3 x 6 matrix, like so: $\begin{matrix} 2 & 3 & 1 & 1 & 0 & 0 \\ 3 & 3 & 1 & 0 & 1 & 0 \\ 2 & 4 & 1 & 0 & 0 & 1 \end{matrix}$ Then, you use GJ elimination methods until you have $\begin{matrix} 1 & 0 & 0 & a & b &c \\ 0 & 1 & 0 & d &e & f \\ 0 & 0 & 1 & g & h & i \end{matrix}$ Take that 3x3 matrix on the right, multiply it by 1 over the determinant of your original matrix, and you are done!

9. anonymous

Are u sure you have to use the determinant can u just use elimination?

10. anonymous

cuz we didnt learn abt that yet really

11. anonymous

Only in next chapter

12. anonymous

Sorry, you don't need to divide by the determinant, my bad.

13. anonymous

lol Thnx

14. anonymous

15. anonymous

No problem! :) Also, this method is how you find the inverses of matrices in general. You'll note that if you try to solve the standard 2x2 matrix with this method, you will get the inverse that you probably learned in class. There are some slightly easier techniques to solve 3x3 matrices, but the proof of the validity of that method requires some linear algebra. Besides, this method always works!

16. anonymous

Thanks