STEP 3:
Remember that our goal is the make the left side the identity matrix...
![[ row 1: 2 , 0 row 2: 0 , 1 | row 1: -5 , -3 row 2: 2 , 1 ] ... make the 2 and the 1 in the left half one's](/sites/default/files/images/06-matrices-19.gif)
This guy is already OK.
![[ row 1: 1 , 0 row 2: 0 , 1 | row 1: -( 5 / 2 ) , -( 3 / 2 ) row 2: 2 , 1 ] ... ( 1 / 2 ) times Row 1 ... believe it or not, the right half should be A^( -1 )](/sites/default/files/images/06-matrices-20.gif)
![A^( -1 ) = [ row 1: -( 5 / 2 ) , -( 3 / 2 ) row 2: 2 , 1 ]](/sites/default/files/images/06-matrices-21.gif)
So... how do we know for sure?
Well, think back to regular numbers for a minute...
| What's |  |
? | |
|
|
 |
the multiplicative inverse | |
With letters...
| So |  |