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3. Tenglamalar sistemasining echimlarini toping: \( \left\{\begin{array}{l}x_{1}+2 x_{2}-x_{3}+2 x_{4}=4 \\ 2 x_{1}+3 x_{2}+4 x_{3}-x_{4}=8 \\ -5 x_{1}+x_{2}-3 x_{3}=-7 \\ x_{2}+x_{3}-7 x_{4}=-5\end{array}\right. \)

Ask by Cruz Norton. in Uzbekistan
Dec 18,2024

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Tenglamalar sistemasining yechimlari: \[ \begin{cases} x_{1} = 1 \\ x_{2} = 1 \\ x_{3} = 1 \\ x_{4} = 1 \\ \end{cases} \]

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Berilgan tenglamalar sistemasining yechimlari quyidagicha: \[ \begin{cases} x_{1} = 1 \\ x_{2} = 1 \\ x_{3} = 1 \\ x_{4} = 1 \\ \end{cases} \] **Yechimlar:** - \( x_{1} = 1 \) - \( x_{2} = 1 \) - \( x_{3} = 1 \) - \( x_{4} = 1 \) Siz ushbu qiymatlarni har bir tenglamaga qo'yib, tekshirishingiz mumkin. Barcha tenglamalarda tengliklar to'g'ri keladi.

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Birinchi navbatda, tenglamalar sistemasini matritsa ko'rinishiga o'tkazamiz va Gauss eliminasiyasi usulini qo'llab yechimlarni topishga harakat qilamiz. Har bir tenglamani ko'rsatilgan formatda yozamiz va ushbu matritsani ko'rinishiga keltiramiz. Shundan so'ng, bosqichma-bosqich oddiylashtirish orqali yechimlarni aniqlaymiz. Endi yechimlarni ko'rib chiqaylik. Bunday muammolarni yechishda eng ko'p uchraydigan xatolardan biri, matritsani manipulyatsiya qilishda hisob-kitoblar vaqtida noaniqliklar kiritishdir. Har bir qadamda bajarilgan amallarni diqqat bilan tekshirib boring va takrorlanadigan jarayonlarda o'zingizga ma'lum bir tizimni o'rnating!

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