Mencari A−1 menggunakan kaedah Adjoin

1. Cari minor

M 11=|a b cd e fg h i| =|e f

h i|=ef−h i

M 23=|a b cd e fg h i| =|a b

g h|=ab−gh

2. Cari kofaktor

C11=(−1)1+1M 11=M11

C23=(−1)2+3M 23=−M 23

3. Bina matriks kofaktor

Matriks kofaktor =[c11 c12 c13c21 c22 c23c31 c32 c33]

=[ M 11 −M12 M 13

−M 21 M22 −M 23

M 31 −M32 M 33]

Adj A = [Matrikskofaktor ]T

= [ M 11 −M 21 M 13

−M 12 M22 −M32

M13 −M23 M 33]

A=[ a b cd e fg h i ]

4. Maka A−1= 1|A|

Adj A

Contoh:

|A|=|1 −2 −13 −1 −40 1 2

1 −23 −10 1 |

= -2+0-3-(-12-4+0)

= -5+16

= 11

Matriks kofaktor = [ |−1 −41 2 | −|3 −4

0 2 | |3 −10 1 |

−|−2 −11 2 | |1 −1

0 2 | −|1 −20 1 |

|−2 −1−1 −4| −|1 −1

3 −4| |1 −23 −1| ]

=[2 −6 33 2 17 1 5]

Adj A =[ 2 3 7−6 2 13 1 5]

A−1=111 [ 2 3 7

−6 2 13 1 5]

A=[1 −2 −13 −1 −40 1 2 ]