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Inverse Matrices

Let's do another one:

A = [ row 1: -10 , 7 row 2: 4 , -2 ]
 

[ row 1: -10 , 7 row 2: 4 , -2 | row 1: 1 , 0 row 2: 0 , 1 ]


STEP 1:

      use the -10 on the left ... to ditch the 4 on the left ... [ row 1: -10 , 7 row 2: 4 , -2 | row 1: 1 , 0 row 2: 0 , 1 ]

We'll need to adjust both rows to get these numbers to be the same, but with opposite signs.

         2 times Row 1 ... 5 times Row 2 ... [ row 1: -20 , 14 row 2: 20 , -10 | row 1: 2 , 0 row 2: 0 , 5 ]
    * The most common mistake is to forget to work your way all the way across!

Row 1 back
to normal

Row 1 +
Row 2

[ row 1: -10 , 7 row 2: 0 , 4 | row 1: 1 , 0 row 2: 2 , 5 ]

 

STEP 2:

        1) use the 4 on the left side ... 2) to ditch the 7 on the left side ... [ row 1: -10 , 7 row 2: 0 , 4 | row 1: 1 , 0 row 2: 2 , 5 ]

 

     4 times Row 1 ... -7 times Row 2 ... [ row 1: -40 , 28 row 2: 0 , -28 | row 1: 4 , 0 row 2: -14 , -35 ]

 

Row 2 +
Row 1

Row 1 back
to normal

[ row 1: -40 , 0 row 2: 0 , 4 | row 1: -10 , -35 row 2: 2 , 5 ]