1. ## Find K

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?

2. 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 \, ....
$

3. Originally Posted by mr fantastic
$
\begin{vmatrix}
0 & c & b\\
c & 0 & a \\
b & a & 0
\end{vmatrix} = 0 \, ....
$
and

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

4. $
\begin{vmatrix}
0 & c & b\\
c & 0 & a \\
b & a & 0
\end{vmatrix} = 2abc
$

6. 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.

7. Originally Posted by zorro
Look at post #3 and post #4 and draw the obvious conclusion.

8. 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

9. 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 ....

$
\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
$

11. 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
$
..