prove that |a b ax+by | |b c bx+cy | |ax+by bx+cy 0 | =(b^2-ac)(ax^2+2bxy+cy^2)
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Originally Posted by minaxijgupta prove that |a b ax+by | |b c bx+cy | |ax+by bx+cy 0 | =(b^2-ac)(ax^2+2bxy+cy^2) Compute this determinant by using the 3rd collossus. Thus, we have, Thus, Thus, Now, just open this expression up and also open up the expression you are trying to prove to see that they match!
Originally Posted by ThePerfectHacker ... Thus, Thus, Now, just open this expression up and also open up the expression you are trying to prove to see that they match! Hello, with this result (which I never would have found) I suggest factorization: And now, minaxijgupta, the next steps are for you. Best wishes EB
Hello, minaxijgupta! I think I've come up with a good approach . . . Prove that: . Perform some row operations to simplify the determinant . . . Now we "expand by minors" (using the top row): . . . . . . . . . ta-DAA!
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