123456789
of 9

Inverse Matrices

STEP 1:

      use the 2 on the left ... to ditch the -4 on the left ... [ row 1: 2 , 3 row 2: -4 , -5 | row 1: 1 , 0 row 2: 0 , 1 ]                       

We want these two numbers to be the same, but have opposite signs.  Then, we'll add them together and get 0.

              2 times Row 1 ... [ row 1: 4 , 6 row 2: -4 , -5 | row 1: 2 , 0 row 2: 0 , 1 ] ... Work all the way across!

Now, we add Row 1 and Row 2 -- just work straight down!  Then, you put Row 1 back to normal:

Row 1 back to normal

Row 1 +
Row 2

[ row 1: 2 , 3 row 2: 0 , 1 | row 1: 1 , 0 row 2: 2 , 1 ]

 

STEP 2:

Now, we work a bit backwards!

             1) use the 1 in the left half ... 2) to ditch the 3 in the left half ... [ row 1: 2 , 3 row 2: 0 , 1 | row 1: 1 , 0 row 2: 2 , 1 ]

We want these two numbers to be the same, but have opposite signs.  Then, we'll add them together and get 0.

       [ row 1: 2 , 3 row 2: 0 , -3 | row 1: 1 , 0 row 2: -6 , -3 ] ... -3 times Row 2

Now, we add Row 1 and Row 2 -- just work straight up!  Then, you put Row 2 back to normal:

 

Row 2 +
Row 1

Row 2 back to normal

   [ row 1: 2 , 0 row 2: 0 , 1 | row 1: -5 , -3 row 2: 2 , 1 ]