mencari a
Post on 09-Apr-2016
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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 ]
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