Reja Matritsalar algebrasining elementlari

Misollar. Matritsaviy ifodaning qiymatini toping:

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Nazorat savollari
1. Matritsaga ta’rif bering. Matritsaning tuzilishi nimadan iborat?

2. Diagonal matritsaning ko‘rinishini yozing.

3. Birlik matritsaning ko‘rinishini yozing.

4. Matritsalarning tengligiga va teng emasligiga ta’rif bering.

5. Maxsus va maxsusmas matritsalarga ta’rif bering.

6. Berilgan matritsalarni qo‘shish, ayirish va songa ko‘paytirish qanday bajariladi?

7. Matritsalarni ko‘paytirish amalini tushuntiring.

Teskari matritsa
Ushbu

matritsa uchun teskari matritsani topaylik. Buning uchun, avvalo, determinantni yozamiz va uni hisoblaymiz:

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Demak, A – maxsusmas matritsa, unga teskari matritsa mavjud. Endi, ning har bir satr algebraik to‘ldiruvchilarini hisoblaymiz:

A₁₁ = 4^.6 – 5^.5 = -1, A₁₂ = -(2^.6 – 3^.5) = 3, A₁₃ = 2^.5 – 3^.4 = -2,

A₂₁ = -(2^.6 – 5^.3 = 3, A₂₂ = 1^.6 – 3^.3 = -3, A₂₃ = -(5^.1 – 3^.2) = 1,

A₃₁ = 2^.4 – 4^.3 = -2, A₃₂ = -(1^.5 – 3^.2) = 1, A₃₃ = 1^.4 – 2^.2 = 0.

Bularni mos ravishda ustunlar qilib yozib, C^ matritsani tuzamiz:

Nihoyat, C^ ning barcha elementlarini detA=-1 ga bo‘lib teskari matritsaga ega bo‘lamiz:

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Endi, A^.A^-1=E ekanligini tekshiramiz. Haqiqiatdan ham,

Shunga o‘xshash, A^{-1 .}A=E ekani ham ko‘rsatiladi.

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