## Kweku Group Title How do you find the determinant of a 4x4 matrix? one year ago one year ago

1. geerky42 Group Title
2. Kweku Group Title

I didnt get you.

3. novagirl114 Group Title

Do you have a graphing calculator? If so you can input the matrix and the calculator can sovle for the determinant.

4. geerky42 Group Title

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

5. malevolence19 Group Title

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.

6. malevolence19 Group Title

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.