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Math Help - Find K

  1. #1
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    Unhappy Find K

    Given

    <br />
\begin{vmatrix}<br />
b^2 + c^2 & ab & ac \\<br />
ba & c^2+a^2 & bc \\<br />
ca & cb & b^2+a^2<br />
\end{vmatrix}<br />
= <br />
\begin{vmatrix}<br />
0 & c & b\\<br />
c & 0 & a \\<br />
b & a & 0<br />
\end{vmatrix}<br />
= <br />
K a^2 b^2 c^2<br />
    Find K?
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  2. #2
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    Quote Originally Posted by zorro View Post
    Given

    <br />
\begin{vmatrix}<br />
b^2 + c^2 & ab & ac \\<br />
ba & c^2+a^2 & bc \\<br />
ca & cb & b^2+a^2<br />
\end{vmatrix}<br />
= <br />
\begin{vmatrix}<br />
0 & c & b\\<br />
c & 0 & a \\<br />
b & a & 0<br />
\end{vmatrix}<br />
= <br />
K a^2 b^2 c^2<br />
    Find K?
    <br />
\begin{vmatrix}<br />
0 & c & b\\<br />
c & 0 & a \\<br />
b & a & 0<br />
\end{vmatrix} = 0 \, ....<br />
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    <br />
\begin{vmatrix}<br />
0 & c & b\\<br />
c & 0 & a \\<br />
b & a & 0<br />
\end{vmatrix} = 0 \, ....<br />
    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
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  4. #4
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    <br />
\begin{vmatrix}<br />
0 & c & b\\<br />
c & 0 & a \\<br />
b & a & 0<br />
\end{vmatrix} = 2abc <br />
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  5. #5
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    Whatz the answer

    What is the Answer
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  6. #6
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    Quote Originally Posted by mr fantastic View Post
    <br /> <br />
\begin{vmatrix}<br /> <br />
0 & c & b\\<br /> <br />
c & 0 & a \\<br /> <br />
b & a & 0<br /> <br />
\end{vmatrix} = 0 \, ....<br /> <br />
    Quote Originally Posted by Rapha View Post
    <br />
\begin{vmatrix}<br />
0 & c & b\\<br />
c & 0 & a \\<br />
b & a & 0<br />
\end{vmatrix} = 2abc <br />
    Whoops. My careless mistake. Thanks for the catch.
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  7. #7
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    Quote Originally Posted by zorro View Post
    What is the Answer
    Look at post #3 and post #4 and draw the obvious conclusion.
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  8. #8
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    Quote Originally Posted by zorro View Post
    Given

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


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

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

    and

    <br />
\begin{vmatrix}<br />
0 & c & b\\<br />
c & 0 & a \\<br />
b & a & 0<br />
\end{vmatrix}<br />
= -a+2abc

    please tell me what i did wrong
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  9. #9
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    Quote Originally Posted by zorro View Post
    I am getting some other answer........

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

    and

    <br />
\begin{vmatrix}<br />
0 & c & b\\<br />
c & 0 & a \\<br />
b & a & 0<br />
\end{vmatrix}<br />
= -a+2abc

    please tell me what i did wrong
    Can you explain hw you got those answers - the second one in particular ....
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  10. #10
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    here my answer

    <br />
\begin{vmatrix}<br />
0 & c & b \\<br />
c & 0 & a \\<br />
b & a & 0<br />
\end{vmatrix}<br />
= <br />
0(0-a)-c(0-ab)+b(ca-0)<br />
= <br />
-a+abc+abc<br />
= <br />
-a+2abc<br />
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  11. #11
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    Quote Originally Posted by zorro View Post
    <br />
\begin{vmatrix}<br />
0 & c & b \\<br />
c & 0 & a \\<br />
b & a & 0<br />
\end{vmatrix}<br />
= <br />
0(0-a)-c(0-ab)+b(ca-0) Mr F says: 0(0 - a) = 0.
    = <br />
-a+abc+abc<br />
= <br />
-a+2abc<br />
    ..
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