Abdishukurov shaxzod

Matritsalar va ular ustida amallar

𝐴𝐵 ko’paytmaning mavjudligidan 𝐵𝐴 ko’paytmaning mavjudligi kelib chiqmaydi. 𝐴𝐵 va 𝐵𝐴 ko’paytmalar mavjud bo’lgan taqdirda ham, odatda (ko’p hollarda), 𝐴𝐵 va 𝐵𝐴 ko’paytmalar bir-biriga teng bo’lmaydi: 𝐴𝐵 ≠ 𝐵𝐴. Agar 𝐴𝐵 = 𝐵𝐴 bo’lsa, u holda 𝐴 va 𝐵 matritsalar o’zaro o’rin almashinuvchi (kommutativ) matritsalar deyiladi.

Ma’lumki, har doim 𝐴𝐵 𝐶 = 𝐴 𝐵𝐶 tenglik o’rinli.

Matritsalar va ular ustida amallar

Misol 1. 𝐴𝐵 va 𝐵𝐴 ko’paytmalarni toping.

𝐴 =

4 −5 8

1 3 −1

,

𝐵 =

−1 5

−2 −3

3 4

.

𝐴𝐵 ko’paytmani topamiz:

𝐴𝐵 =

4 −5 8

1 3 −1

⋅

−1 5

−2 −3

3 4

=

=

4 ⋅ (−1) + (−5) ⋅ (−2) + 8 ⋅ 3

1 ⋅ (−1) + 3 ⋅ (−2) + (−1) ⋅ 3

4 ⋅ 5 + (−5) ⋅ (−3) + 8 ⋅ 4

1 ⋅ 5 + 3 ⋅ (−3) + (−1) ⋅ 4

=

30 67

−10 −8

.