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Inverse Matrices

STEP 3:

      turn the -40 and the 4 on the left side into one's ... [ row 1: -40 , 0 row 2: 0 , 4 | row 1: -10 , -35 row 2: 2 , 5 ]

 

  -( 1 / 40 ) times Row 1 ... 1 / 4 times Row 2 ... [ row 1: 1 , 0 row 2: 0 , 1 | row 1: ( -10 / -40 ) , ( -35 / -40 ) row 2: ( 2 / 4 ) , ( 5 / 4 ) ]

 

SoA^( -1 ) = [ row 1: ( 1 / 4 ) , ( 7 / 8 ) row 2: ( 1 / 2 ) , ( 5 / 4 ) ]

Let's check it!

A^( -1 ) times A

[ row 1: -10 , 7 row 2: 4 , 2 ] times [ row 1: ( 1 / 4 ) , ( 7 / 8 ) row 2: ( 1 / 2 ) , ( 5 / 4 ) ] = [ row 1: 1 , 0 row 2: 0 , 1 ] ... I

Woo hoo!
 

TRY IT:

Find the inverse of this matrix, then check it:

A = [ row 1: 3 , 8 row 2: -6 , 5 ]