Invers, Aturan Aritmatika Matriks

Sifat- sifat Transpos
(( ) =
(A+B) = + dan (A B) =
(k ) = , dengan k adalah skalar sebarang
( ) =

Invers, Aturan Aritmatika Matriks
Sifat operasi matriks untuk bilangan real a dan b, selalu berlaku ab=ba yang disebut hukum komulatif perkalian. Tetapi untuk matriks, AB dan BA tidak selalu setara.
Contoh sifat aritmatika matriks
Maka ,

Maka ,

Dan ,

Jadi, (AB)C = A(BC) sebagaimana sifat aritmatika matriks.
A = 123401

B = 4321

C = 1023

AB = 123401 4321=85201321

BC = 43211023=10943

=852013211023=1815463943

=10943123401=1815463943

Sifat sifat aritmatika matriks
A+B = B+A
A+ (B+C) = (A+B) +C
A(BC) = (AB)C
A(B+C) = AB + AC
(B+C)A = BA + BC
A(B-C) = AB – AC
(B-C)A = BA – BC
a(B+C) = aB + aC
A(B-C) = aB - aC

(Hukum komulatif penjumlahan)
(Hukum assosiatif penjumlahan)
(Hukum assosiatif perkalian)
(Hukum distributif kiri)
(Hukum distributif kanan)

(a+b)C = aC + bC
(a-b)C = aC – bC
a(bC) = (ab)C
a(BC) = (aB)C = B(aC)
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Second level
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Second level
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Second level
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Fourth level
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Second level
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Fifth level
25/02/2015

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25/02/2015

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Second level
Third level
Fourth level
Fifth level
25/02/2015

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25/02/2015

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25/02/2015

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Second level
Third level
Fourth level
Fifth level
25/02/2015

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Invers, Aturan Aritmatika Matriks

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