Calculate the determinant of the following matrix

0 6 2 -4 3 -6

2 1 -1 2 1 -1

0 3 1 -2 -5 -3

-1 1 3 1 α -1

3 1 -1 2 1 -1

6 0 β 1 0 2

Thankyou in adavance for any assistance provided

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- May 17th 2009, 07:42 AMspeckmagooDeterminant
Calculate the determinant of the following matrix

0 6 2 -4 3 -6

2 1 -1 2 1 -1

0 3 1 -2 -5 -3

-1 1 3 1 α -1

3 1 -1 2 1 -1

6 0 β 1 0 2

Thankyou in adavance for any assistance provided - May 17th 2009, 08:40 AMMush
- May 17th 2009, 09:01 AMspeckmagooReply
Thankyou for your assistance Mush.

Unfortunately, i have to do this by hand. Would it be possible for you to describe the steps you took in order to derive your solution (-728). - May 17th 2009, 09:08 AMMoo
- May 17th 2009, 09:18 AMspeckmagooReply
Thankyou for your assistance Moo, i guess if you are willing and able to show me 2 pages of solutions, then i would be happy to do that.

- May 17th 2009, 09:20 AMMoo
- May 17th 2009, 09:31 AMspeckmagooReply
My misunderstanding(Rofl), its not that i want to do a 2 page solution to this question, its purely out of necessity in answering an assignment question unfortunately(Headbang). How confident are you that the answer is in fact -728? Just to be sure, i hope the characters alpha (4th row, 5th column) and beta (6th row, 3rd column) amongst the other intergers within the array, have been taken into account, and not misinterpreted in any manner.

- May 17th 2009, 06:03 PMawkward
- May 17th 2009, 06:47 PMawkward
- May 17th 2009, 08:12 PMKrizalid
it's a lot of boring work!! but yes, it's $\displaystyle -728$ the answer.

let me introduce you another example so you can follow the process and apply it in your problem: let $\displaystyle A\in\mathbb M_4$ be matrix such that $\displaystyle A=\left[ \begin{matrix}

1 & 2 & 3 & 4 \\

2 & 2 & 3 & 4 \\

3 & 3 & 3 & 4 \\

4 & 4 & 4 & 4

\end{matrix} \right],$ now let's compute $\displaystyle |A|,$

$\displaystyle \left| A \right|\overset{R_{2}-R_{1}}{\mathop{=}}\,\left| \begin{matrix}

1 & 2 & 3 & 4 \\

1 & 0 & 0 & 0 \\

3 & 3 & 3 & 4 \\

4 & 4 & 4 & 4

\end{matrix} \right|=-\left| \begin{matrix}

2 & 3 & 4 \\

3 & 3 & 4 \\

4 & 4 & 4

\end{matrix} \right|=-\left| \begin{matrix}

2 & 3 & 4 \\

1 & 0 & 0 \\

4 & 4 & 4

\end{matrix} \right|=\left| \begin{matrix}

3 & 4 \\

4 & 4 \\

\end{matrix} \right|=-4.$

does this make sense? the thing is: make zeros and then apply cofactors according to the row or column you created zeros.