Find K

**zorro** · December 30th 2008, 12:23 AM

Given

$ \begin{vmatrix} b^2 + c^2 & ab & ac \\ ba & c^2+a^2 & bc \\ ca & cb & b^2+a^2 \end{vmatrix} $ = $ \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix} $ = $ K a^2 b^2 c^2 $
Find K?

**mr fantastic** · December 30th 2008, 01:07 AM

Originally Posted by zorro

Given

$ \begin{vmatrix} b^2 + c^2 & ab & ac \\ ba & c^2+a^2 & bc \\ ca & cb & b^2+a^2 \end{vmatrix} $ = $ \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix} $ = $ K a^2 b^2 c^2 $
Find K?

$ \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix} = 0 \, .... $

**Rapha** · December 30th 2008, 02:26 AM

Originally Posted by mr fantastic

$ \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix} = 0 \, .... $

and

$\begin{vmatrix}b^2 + c^2 & ab & ac \\ba & c^2+a^2 & bc \\ca & cb & b^2+a^2 \end{vmatrix} = ... = 4a^2b^2c^2$

**Rapha** · December 30th 2008, 02:30 AM

$ \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix} = 2abc $

**zorro** · December 30th 2008, 02:54 AM

What is the Answer

**mr fantastic** · December 30th 2008, 12:24 PM

Originally Posted by mr fantastic

$ \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix} = 0 \, .... $

Originally Posted by Rapha

$ \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix} = 2abc $

Whoops. My careless mistake. Thanks for the catch.

**mr fantastic** · December 30th 2008, 01:05 PM

Originally Posted by zorro

What is the Answer

Look at post #3 and post #4 and draw the obvious conclusion.

**zorro** · December 30th 2008, 10:58 PM

Originally Posted by zorro

Given

$ \begin{vmatrix} b^2 + c^2 & ab & ac \\ ba & c^2+a^2 & bc \\ ca & cb & b^2+a^2 \end{vmatrix} $ = $ \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix} $ = $ K a^2 b^2 c^2 $
Find K?

I am getting some other answer........

$ \begin{vmatrix} b^2 + c^2 & ab & ac \\ ba & c^2+a^2 & bc \\ ca & cb & b^2+a^2 \end{vmatrix} $ = $3a^2b^2c^2 + a^2bc^3 + a^4bc$

and

$ \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix} $ = $-a+2abc$

please tell me what i did wrong

**mr fantastic** · December 30th 2008, 11:11 PM

Originally Posted by zorro

I am getting some other answer........

$ \begin{vmatrix} b^2 + c^2 & ab & ac \\ ba & c^2+a^2 & bc \\ ca & cb & b^2+a^2 \end{vmatrix} $ = $3a^2b^2c^2 + a^2bc^3 + a^4bc$

and

$ \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix} $ = $-a+2abc$

please tell me what i did wrong

Can you explain hw you got those answers - the second one in particular ....

**zorro** · December 31st 2008, 07:33 PM

$ \begin{vmatrix} 0 & c & b \\ c & 0 & a \\ b & a & 0 \end{vmatrix} $ = $ 0(0-a)-c(0-ab)+b(ca-0) $ = $ -a+abc+abc $ = $ -a+2abc $

**mr fantastic** · December 31st 2008, 09:35 PM

Originally Posted by zorro

$ \begin{vmatrix} 0 & c & b \\ c & 0 & a \\ b & a & 0 \end{vmatrix} $ = $ 0(0-a)-c(0-ab)+b(ca-0)$ Mr F says: 0(0 - a) = 0.
= $ -a+abc+abc $ = $ -a+2abc $

..

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