# 4 x 4 determinant

• May 24th 2010, 11:42 AM
renlok
4 x 4 determinant
I had the question solve the determinate: $\displaystyle \begin{vmatrix}7 & 11 & 13 & 17\\ 11 & 13 & 17 & 13\\ 13 & 17 & 13 & 11\\ 17 & 13 & 11 & 7\end{vmatrix}$

I know how to do it the normal way of splitting it into 3 x3 determinate then spiting them into 2 x 2. But this is a question from a non-calculator exam, i looked at the answer and in the answer it says you need to reduce it to
$\displaystyle 24\begin{vmatrix}4 & 13 & 24\\ -1 & 2 & 0\\ -4 & -1 & 0\end{vmatrix}$
but ive no clue how to do this im pretty sure we've never been told could someone help me out please
• May 24th 2010, 02:15 PM
awkward
Quote:

Originally Posted by renlok
I had the question solve the determinate: $\displaystyle \begin{vmatrix}7 & 11 & 13 & 17\\ 11 & 13 & 17 & 13\\ 13 & 17 & 13 & 11\\ 17 & 13 & 11 & 7\end{vmatrix}$

I know how to do it the normal way of splitting it into 3 x3 determinate then spiting them into 2 x 2. But this is a question from a non-calculator exam, i looked at the answer and in the answer it says you need to reduce it to
$\displaystyle 24\begin{vmatrix}4 & 13 & 24\\ -1 & 2 & 0\\ -4 & -1 & 0\end{vmatrix}$
but ive no clue how to do this im pretty sure we've never been told could someone help me out please

I don't know if I can get the answer into the form of "the answer", but it looks like a good way to start is to subtract row 1 from rows 2, 3, and 4, and then add column 4 to column 1. After that you should be in good shape to expand by minors about column 1.
• May 24th 2010, 02:37 PM
Also sprach Zarathustra
Quote:

Originally Posted by renlok
I had the question solve the determinate: $\displaystyle \begin{vmatrix}7 & 11 & 13 & 17\\ 11 & 13 & 17 & 13\\ 13 & 17 & 13 & 11\\ 17 & 13 & 11 & 7\end{vmatrix}$

I know how to do it the normal way of splitting it into 3 x3 determinate then spiting them into 2 x 2. But this is a question from a non-calculator exam, i looked at the answer and in the answer it says you need to reduce it to
$\displaystyle 24\begin{vmatrix}4 & 13 & 24\\ -1 & 2 & 0\\ -4 & -1 & 0\end{vmatrix}$
but ive no clue how to do this im pretty sure we've never been told could someone help me out please

$\displaystyle \begin{vmatrix}7 & 11 & 13 & 17\\ 11 & 13 & 17 & 13\\ 13 & 17 & 13 & 11\\ 17 & 13 & 11 & 7\end{vmatrix}=72^2$