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Exercise 32.3

Find the inverse to the matrix B whose rows are first ( 2 4 ) ; second ( 1 3 ) .

Solution:

Here are the rows of the matrices starting with B and with I at each stage of the computation,

Start = stage 0
row 1 of B : ( 2 , 4 ) row 1 of I : ( 1 , 0 )
row 2 of B : ( 1 , 3 ) row 2 of I : ( 0 , 1 )

Step 1: divide row 1 by 2
row 1 of B : ( 1 , 2 ) row 1 of I : ( 1 2 , 0 )
row 2 of B : ( 1 , 3 ) row 2 of I : ( 0 , 1 )

Step 2: subtract row 1 from row 2 and replace row 2 by the result
row 1 of B : ( 1 , 2 ) row 1 of I : ( 1 2 , 0 )
row 2 of B : ( 0 , 1 ) row 2 of I : ( − 1 2 , 1 )

Step 3: subtract twice row 2 from row 1 and replace row 1 by the result
row 1 of B : ( 1 , 0 ) row 1 of I : ( 3 2 , − 2 )
row 2 of B : ( 0 , 1 ) row 2 of I : ( − 1 2 , 1 )

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