4 x 4 determinant

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

awkward

MHF Hall of Honor
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.

Also sprach Zarathustra

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