anonymous
  • anonymous
How do you find the determinant of a 4x4 matrix?
Mathematics
chestercat
  • chestercat
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geerky42
  • geerky42
http://lmgtfy.com/?q=How+do+you+find+the+determinant+of+a+3x3+matrix%3F
anonymous
  • anonymous
I didnt get you.
anonymous
  • anonymous
Do you have a graphing calculator? If so you can input the matrix and the calculator can sovle for the determinant.

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geerky42
  • geerky42
You edited your question... Just Google it or do what @novagirl114 said. http://lmgtfy.com/?q=How+do+you+find+the+determinant+of+a+4x4+matrix%3F
anonymous
  • anonymous
Cofactor expansion. The same way you do 3x3's. If you have: \[A=\left[\begin{matrix}a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31}&a_{32}&a_{33}\end{matrix}\right]\] Then: \[\det(A)=a_{11} \det \left[\begin{matrix}a_{22} & a_{23} \\ a_{32} & a_{33}\end{matrix}\right]-a_{12} \det \left[\begin{matrix}a_{21} & a_{23} \\ a_{31} & a_{33}\end{matrix}\right]+a_{13} \det \left[\begin{matrix}a_{21} & a_{22} \\ a_{31} & a_{32}\end{matrix}\right]\] Better notation is my opinion for an nxn matrix is: \[\det(A)=\sum_{i_1,i_2,...,i_n} \epsilon_{i_1,i_2,...,i_n}a_{1,i_1}a_{2,i_2}...a_{n,i_n}\] Where epsilon is the Levi Cevita tensor.
anonymous
  • anonymous
But the only difference for a 4x4 is that the "sub determinants" (i.e., my determinants of 2x2's) will be THREE BY THREES! So you'll need to do a cofactor expansion to get 4, 3x3 determinants and then 4 cofactor expansions to get 3,2x2 determinants for EACH sub determinant.

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