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If we have a matrix
![A = [ row 1: 2 , 3 row 2: -4 , -5 ]](images/06-matrices-07.gif)
We can't write
-- a result would require division.
So... Can we
find
 ?
We sure can!
It's called an inverse matrix. Here's how you find it:
Let's start with this
matrix
![A = [ row 1: 2 , 3 row 2: -4 , -5 ]](images/06-matrices-10.gif)
This is going to work
a lot like Gaussian elimination. (If you've ever seen that
before.)
We make a big double
matrix
![[ row 1: 2 , 3 row 2: -4 , -5 | row 1: 1 , 0 row 2: 0 , 1 ]](images/06-matrices-11.gif)
A
on this side...
the identity on this side.
The goal is to use
row operations (like you did with Gaussian elimination) to...
![[ row 1: 2 , 3 row 2: -4 , -5 | row 1: 1 , 0 row 2: 0 , 1 ] ... turn the left half into I ... and, in the process, the right half with turn into A^( -1 )](images/06-matrices-12.gif)
Continued on the
next
page
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