# determinant question 5

• November 16th 2010, 12:35 PM
transgalactic
determinant question 5
if $\begin{vmatrix}
a & b &c \\
d & e &f \\
g&h &k
\end{vmatrix}$
=2

then
$\begin{vmatrix}
f & k-4c &2k+f \\
d & g-4a &2g+d \\
e&h-4b &2h+e
\end{vmatrix}$
=-16

is it true?
• November 16th 2010, 05:41 PM
Drexel28
Quote:

Originally Posted by transgalactic
if $\begin{vmatrix}
a & b &c \\
d & e &f \\
g&h &k
\end{vmatrix}$
=2

then
$\begin{vmatrix}
f & k-4c &2k+f \\
d & g-4a &2g+d \\
e&h-4b &2h+e
\end{vmatrix}$
=-16

is it true?

I don't know, is it?
• November 16th 2010, 09:22 PM
transgalactic
i dont know how to break the big determinant into smaller packages of the original determinant
• November 18th 2010, 08:38 PM
Anthonny
Have you tried computing the determinants for both and comparing them? Although I'm not completely sure if this is the best way, but it may work.
• November 18th 2010, 09:01 PM
tonio
Quote:

Originally Posted by Drexel28
I don't know, is it?

Remember that determinant is a multilineal functions, so:

$\begin{vmatrix}f & k-4c &2k+f \\ d & g-4a &2g+d \\ e&h-4b &2h+e \end{vmatrix}=\begin{vmatrix}f & k &2k \\ d & g &2g \\ e&h &2h \end{vmatrix}+\begin{vmatrix}f & k &f \\ d & g &d \\ e&h &e \end{vmatrix}+$ $\begin{vmatrix}f & -4c &2k \\ d & -4a &2g \\ e&-4b &2h \end{vmatrix}+\begin{vmatrix}f & -4c &f \\ d & -4a &d \\ e&-4b &e \end{vmatrix}$ ,

So....??

Tonio
• November 18th 2010, 09:11 PM
Drexel28
Quote:

Originally Posted by tonio
Remember that determinant is a multilineal functions, so:

$\begin{vmatrix}f & k-4c &2k+f \\ d & g-4a &2g+d \\ e&h-4b &2h+e \end{vmatrix}=\begin{vmatrix}f & k &2k \\ d & g &2g \\ e&h &2h \end{vmatrix}+\begin{vmatrix}f & k &f \\ d & g &d \\ e&h &e \end{vmatrix}+$ $\begin{vmatrix}f & -4c &2k \\ d & -4a &2g \\ e&-4b &2h \end{vmatrix}+\begin{vmatrix}f & -4c &f \\ d & -4a &d \\ e&-4b &e \end{vmatrix}$ ,

So....??

Tonio

Why did you quote me? I know how to do this.
• November 18th 2010, 09:14 PM
tonio
Quote:

Originally Posted by Drexel28
Why did you quote me? I know how to do this.

I'm a selective reader(Giggle): only got "I don't know" and thought it was the OP.(Headbang) Hopefully I won't confuse him/her.

Tonio
• November 18th 2010, 10:50 PM
matheagle
I'd do column reduction and then factor out the 2 and -4, so 2(2)(-4)=-16