Use row operations to show that the inverse of the 2*2 matrix:(adsbygoogle = window.adsbygoogle || []).push({});

[ a , b ]

[ c , d ]

is the matrix (1/(ad-bc))[ d , -b ]

[ -c , a ]

provided that ad-bc =/= 0

I created an augmented matrix as follows

[ a , b | 1 , 0 ]

[ c , d | 0 , 1 ]

so no i have to use row operations to make the left hand side an identity matrix...

divide row1 by a and row 2 by c

[ 1 , b/a | 1/a , 0 ]

[ 1 , d/c | 0 , 1/c ]

then row2 minus row1

[ 1 , b/a | 1/a , 0 ]

[ 0 , d/c - b/a | -1/a , 1/c ]

But as what to do from here I'm stumped everything i try just ends up leading me in a circle... like usual any help would be greatly appreciated :)

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# Homework Help: Matrix Inverse Proof (2*2)

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