## Sportaholic013 2 years ago How do you find the determinant of a 4X4 matrix? :)

1. Raja99

ok

2. Raja99

u need to multiply each element of a row with the determinant of the 3x3 matrix

3. UnkleRhaukus

$|A|=\left|\begin{array}{ccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\a_{2,1}&a_{2,2}&a_{2,3}&a_{2,4}\\a_{3,1}&a_{3,2}&a_{3,3}&a_{3,4}\\a_{4,1}&a_{4,2}&a_{4,3}&a_{4,4}\end{array}\right|$ $\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|$

4. Raja99

correct

5. UnkleRhaukus

that was a lots of typing

6. Sportaholic013

Thanks a million that's great :D

7. Sportaholic013

Are the signs also important? ie. + - + - :)

8. Raja99

very imp.. if not the result ll change a lot

9. Sportaholic013

Thank you, and do I multipy the diagonal terms and subtract to get a single figure?

10. UnkleRhaukus

$|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}$

11. Sportaholic013

Thank you I understand it now :)