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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- Jul 5th 2006, 08:12 PMminaxijguptadeterminant
prove that

|a b ax+by |

|b c bx+cy |

|ax+by bx+cy 0 |

=(b^2-ac)(ax^2+2bxy+cy^2) - Jul 5th 2006, 08:32 PMThePerfectHackerQuote:

Originally Posted by**minaxijgupta**

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! - Jul 5th 2006, 09:55 PMearbothQuote:

Originally Posted by**ThePerfectHacker**

with this result (which I never would have found) I suggest factorization:

And now, minaxijgupta, the next steps are for you.

Best wishes

EB - Jul 6th 2006, 07:42 AMSoroban
Hello, minaxijgupta!

I*think*I've come up with a good approach . . .

Quote:

Prove that: .

Perform some row operations to simplify the determinant . . .

Now we "expand by minors" (using the top row):

. .

. .

. .*. . . ta-DAA!*