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How do you find the determinant of a 4X4 matrix? :)

Mathematics
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ok
u need to multiply each element of a row with the determinant of the 3x3 matrix
\[|A|=\left|\begin{array}{ccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\a_{2,1}&a_{2,2}&a_{2,3}&a_{2,4}\\a_{3,1}&a_{3,2}&a_{3,3}&a_{3,4}\\a_{4,1}&a_{4,2}&a_{4,3}&a_{4,4}\end{array}\right|\] \[\quad=a_{1,1}\left|\begin{array}{ccc}\\a_{2,2}&a_{2,3}&a_{2,4}\\a_{3,2}&a_{3,3}&a_{3,4}\\a_{4,2}&a_{4,3}&a_{4,4}\end{array}\right|-a_{1,2}\left|\begin{array}{ccc}\\a_{2,1}&a_{2,3}&a_{2,4}\\a_{3,1}&a_{3,3}&a_{3,4}\\a_{4,1}&a_{4,3}&a_{4,4}\end{array}\right|\]\[\qquad\qquad\qquad+a_{1,3}\left|\begin{array}{ccc}\\a_{2,1}&a_{2,2}&a_{2,4}\\a_{3,1}&a_{3,2}&a_{3,4}\\a_{4,1}&a_{4,2}&a_{4,4}\end{array}\right|-a_{1,4}\left|\begin{array}{ccc}\\a_{2,1}&a_{2,2}&a_{2,3}\\a_{3,1}&a_{3,2}&a_{3,3}\\a_{4,1}&a_{4,2}&a_{4,3}\end{array}\right|\]

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Other answers:

correct
that was a lots of typing
Thanks a million that's great :D
Are the signs also important? ie. + - + - :)
very imp.. if not the result ll change a lot
Thank you, and do I multipy the diagonal terms and subtract to get a single figure?
\[|B|=\left|\begin{array}{ccc}b_{1,1}&b_{1,2}&b_{1,3}\\b_{2,1}&b_{2,2}&b_{2,3}\\b_{3,1}&b_{3,2}&b_{3,3}\end{array}\right|\]\[\qquad =b_{1,1}\left|\begin{array}{ccc}b_{2,2}&b_{2,3}\\b_{3,2}&b_{3,3}\end{array}\right|-b_{1,2}\left|\begin{array}{ccc}b_{2,1}&b_{2,3}\\b_{3,1}&b_{3,3}\end{array}\right|+b_{1,3}\left|\begin{array}{ccc}b_{2,1}&b_{2,2}\\b_{3,1}&b_{3,2}\end{array}\right|\] \[|C|=\left|\begin{array}{ccc}c_{1,1}&c_{1,2}\\c_{2,1}&c_{2,2}\end{array}\right|\]\[\qquad=c_{1,1}c_{2,2}-c_{1,2}c_{2,1}\]
Thank you I understand it now :)

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