Re: Problems calculating matrix determinant
- From: magidin@xxxxxxxxxxxxxxxxx (Arturo Magidin)
- Date: Thu, 20 Oct 2005 16:38:09 +0000 (UTC)
In article <dj8glu$1j1$1@xxxxxxxxxxxxxxxxx>, Paminu <asdad@xxxxxxx> wrote:
>I am trying to calculate a determinant of a matrix. But I can't seem to get
>the result to match the one found in my book. Hope someone can give me a
>hint on what I am doing wrong.
>
>http://photos3.blogger.com/blogger/3626/1346/1600/det1.JPG
You have trouble computing products of three binomials, is what you
are doing wrong.
You are trying to calculate the determinant
| a^2 a 1 |
| b^2 b 1 |
| c^2 c 1 |
You tried doing it directly; the book says it is equal to
(a-b)(a-c)(b-c).
The first thing you are doing wrong is that you are not calculating
that product correctly. You write
(a-b)(a-c)(b-c) = a^2 - 2ac + b^2 + 2bc.
Really?
(a-b)(a-c) = a^2 - ab - ac + bc
(a-b)(a-c)(b-c) = (a^2 - ab - ac + bc)(b-c)
= a^2b - ab^2 - abc + b^2c
-a^2c + abc + ac^2 - bc^2
= a^2 b - ab^2 + b^2c - bc^2 + ac^2 - ac^2.
Nothing near what you claimed that product was, but exactly equal to
what your calculation of the determinant was.
I don't know how you got that (a-b)(a-c)(b-c) was equal to a^2 - 2ac +
b^2 + 2bc. I just can't figure out what you did.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
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Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx
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