]> Exercise 32.3

## 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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