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Sportaholic013

  • 2 years ago

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

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  1. Raja99
    • 2 years ago
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    ok

  2. Raja99
    • 2 years ago
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    u need to multiply each element of a row with the determinant of the 3x3 matrix

  3. UnkleRhaukus
    • 2 years ago
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    \[|A|=\left|\begin{array}{ccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\a_{2,1}&a_{2,2}&a_{2,3}&a_{2,4}\\a_{3,1}&a_{3,2}&a_{3,3}&a_{3,4}\\a_{4,1}&a_{4,2}&a_{4,3}&a_{4,4}\end{array}\right|\] \[\quad=a_{1,1}\left|\begin{array}{ccc}\\a_{2,2}&a_{2,3}&a_{2,4}\\a_{3,2}&a_{3,3}&a_{3,4}\\a_{4,2}&a_{4,3}&a_{4,4}\end{array}\right|-a_{1,2}\left|\begin{array}{ccc}\\a_{2,1}&a_{2,3}&a_{2,4}\\a_{3,1}&a_{3,3}&a_{3,4}\\a_{4,1}&a_{4,3}&a_{4,4}\end{array}\right|\]\[\qquad\qquad\qquad+a_{1,3}\left|\begin{array}{ccc}\\a_{2,1}&a_{2,2}&a_{2,4}\\a_{3,1}&a_{3,2}&a_{3,4}\\a_{4,1}&a_{4,2}&a_{4,4}\end{array}\right|-a_{1,4}\left|\begin{array}{ccc}\\a_{2,1}&a_{2,2}&a_{2,3}\\a_{3,1}&a_{3,2}&a_{3,3}\\a_{4,1}&a_{4,2}&a_{4,3}\end{array}\right|\]

  4. Raja99
    • 2 years ago
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    correct

  5. UnkleRhaukus
    • 2 years ago
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    that was a lots of typing

  6. Sportaholic013
    • 2 years ago
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    Thanks a million that's great :D

  7. Sportaholic013
    • 2 years ago
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    Are the signs also important? ie. + - + - :)

  8. Raja99
    • 2 years ago
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    very imp.. if not the result ll change a lot

  9. Sportaholic013
    • 2 years ago
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    Thank you, and do I multipy the diagonal terms and subtract to get a single figure?

  10. UnkleRhaukus
    • 2 years ago
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    \[|B|=\left|\begin{array}{ccc}b_{1,1}&b_{1,2}&b_{1,3}\\b_{2,1}&b_{2,2}&b_{2,3}\\b_{3,1}&b_{3,2}&b_{3,3}\end{array}\right|\]\[\qquad =b_{1,1}\left|\begin{array}{ccc}b_{2,2}&b_{2,3}\\b_{3,2}&b_{3,3}\end{array}\right|-b_{1,2}\left|\begin{array}{ccc}b_{2,1}&b_{2,3}\\b_{3,1}&b_{3,3}\end{array}\right|+b_{1,3}\left|\begin{array}{ccc}b_{2,1}&b_{2,2}\\b_{3,1}&b_{3,2}\end{array}\right|\] \[|C|=\left|\begin{array}{ccc}c_{1,1}&c_{1,2}\\c_{2,1}&c_{2,2}\end{array}\right|\]\[\qquad=c_{1,1}c_{2,2}-c_{1,2}c_{2,1}\]

  11. Sportaholic013
    • 2 years ago
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    Thank you I understand it now :)

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