4 x 4 determinant

Oct 2009
36
0
Aberystwyth, Wales
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
Mar 2008
934
409
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.
 
Dec 2009
1,506
434
Russia
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
\(\displaystyle \begin{vmatrix}7 & 11 & 13 & 17\\ 11 & 13 & 17 & 13\\ 13 & 17 & 13 & 11\\ 17 & 13 & 11 & 7\end{vmatrix}=72^2\)