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Consider the 3x3 Vandermonde matrix:
V=[1 x1 x1^2; 1 x2 x2^2; 1 x3 x3^2]
Show that the det(V) = (x2-x1)(x3-x1)(x3-x2)
Sorry for the format. I did R2-R1 and R3-R1 then found the det to be (x2-x1)(x3^2-x1)-(x2^2-x1^2)(x3-x1)
Is this just an algebraic nightmare or did I do something wrong? Thank you!
You've done something wrong. The answer isQuote:
Originally Posted by pakman
.
I hope you took the easy road and expanded along the first column.
That's what I did. I subtracted row 1 from both row 2 and 3 to get 0's in a21 and a31. But then it gets a bit messy from there (Crying)Quote:
Originally Posted by mr fantasticYou've done something wrong. The answer is
I hope you took the easy road and expanded along the first column.
You should have (x2 - x1)(x3^2 - x1^2) - (x2^2 - x1^2)(x3 - x1) ....Quote:
Originally Posted by pakman
= (x2 - x1)(x3 - x1)(x3 + x1) - (x2 - x1)(x2 + x1)(x3 - x1)
= (x2 - x1)(x3 - x1) [(x3 + x1) - (x2 + x1)] = ......
Ahh okay, stupid algebraic mistake. Thanks!