phy1020.DVI

3 3 Matrices

Determinant

The determinant of a 3  3 matrix is given by:

det

0

@

abc

def

ghi

1

ADa.eifh/b.difg/Cc.dheg/: (P.4)

Matrix of Cofactors

The matrix of cofactors is the matrix of signed minors; for a 3  3 matrix, this is

cof

0

@

abc

def

ghi

1

AD

0

@

eifh fgdi dheg

chbi aicg bgah

bfce cdaf aebd

1

A (P.5)

Inverse

Finally, the inverse of a matrix is the transpose of the matrix of cofactors divided by the determinant. For a
3  3 matrix,

0

@

abc

def

ghi

1

A

 1

D

1

a.eifh/b.difg/Cc.dheg/

0

@

eifh chbi bfce

fgdi aicg cdaf

dheg bgah aebd

1

A(P.6)