(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that if ad-bc ≠ 0 then

RREF[a b] = [1 0]

[c d] [0 1]

3. The attempt at a solution

I cannot use any equivalent statements here, and I don't "know" what a determinant is yet so I have to show this in another way.

I start off by saying if ad - bc ≠ 0 then I can say ad - bc = "e" whether it's positive or negative, i'm not sure, is important. So what I tried was using some substitution and got

a = ( e + bc ) / d

b = ( ad -e ) / c

c = ( ad - e ) / b

d = ( e + bc ) / a

and creating a little 2 x 2 matrix with the RHS, it got too messy and I wasn't even sure what I was doing would work so I stopped with that.

then I went back to ad - bc = ±e and tried working on some ideas with inequalities for instance if ad - bc = +e then I know ad > bc and if ad - bc = -e then I know ad < bc and this is where I get stuck. I'm not sure if any of this is on the right track, but as always, i've come to PF to untangle my mangle. Thanks for the help.

The little scribble at the end of the problem statement is supposed to be a 2x2 matrix row reducing to the identity.

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# Homework Help: Show that if ad-bc ≠ 0

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