# Math Help - Determinant

1. ## Determinant

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

2. Originally Posted by speckmagoo
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
You're joking, right?

You aren't doing that by hand are you?

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).

4. Originally Posted by speckmagoo
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).
For the calculations.

Otherwise, you can try to reduce this matrix into an upper triangular form. That would hurt a bit less ^^

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.

6. Originally Posted by speckmagoo
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.
I meant "by giving YOU two blank pieces of paper" so that you have some room to write all your calculations

Surely, there is no point doing this by hand. That's wasting your time

My misunderstanding, 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. 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.

8. Originally Posted by speckmagoo
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
I don't have time to work this out, but it looks like you might start by multiplying row 3 by -2 and adding it to row 1, then expand by minors along row 1. Look for similar simplifications as you proceed, maybe you will get lucky.

9. Originally Posted by awkward
I don't have time to work this out, but it looks like you might start by multiplying row 3 by -2 and adding it to row 1, then expand by minors along row 1. Look for similar simplifications as you proceed, maybe you will get lucky.
On second thought, it looks better to start by adding column 2 to column 6.

10. it's a lot of boring work!! but yes, it's $-728$ the answer.

let me introduce you another example so you can follow the process and apply it in your problem: let $A\in\mathbb M_4$ be matrix such that $A=\left[ \begin{matrix}
1 & 2 & 3 & 4 \\
2 & 2 & 3 & 4 \\
3 & 3 & 3 & 4 \\
4 & 4 & 4 & 4
\end{matrix} \right],$
now let's compute $|A|,$

$\left| A \right|\overset{R_{2}-R_{1}}{\mathop{=}}\,\left| \begin{matrix}
1 & 2 & 3 & 4 \\
1 & 0 & 0 & 0 \\
3 & 3 & 3 & 4 \\
4 & 4 & 4 & 4
\end{matrix} \right|=-\left| \begin{matrix}
2 & 3 & 4 \\
3 & 3 & 4 \\
4 & 4 & 4
\end{matrix} \right|=-\left| \begin{matrix}
2 & 3 & 4 \\
1 & 0 & 0 \\
4 & 4 & 4
\end{matrix} \right|=\left| \begin{matrix}
3 & 4 \\
4 & 4 \\
\end{matrix} \right|=-4.$

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