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Berilgan determinant quyidagicha:

\[
\Delta = \begin{vmatrix} 12 & 23 & 34 & 45 \\ 0 & 21 & 32 & 43 \\ 7 & 7 & 7 & 7 \\ 29 & 29 & 29 & 29 \end{vmatrix}
\]

Bu determinantni hisoblash uchun asosiy xossalarni ko'rib chiqamiz. Determinantning ikki qatori yoki ustunlari bir xil yoki proporsional bo'lsa, determinantning qiymati 0 ga teng bo'ladi.

Uchinchi va to'rtinchi ustunlar o'zaro teng:

\[
\begin{vmatrix} 7 & 7 & 7 & 7 \\ 29 & 29 & 29 & 29 \end{vmatrix}
\]

Bu holda, uchinchi va to'rtinchi qatordagi barcha elementlar bir xil (har bir ustunda ham bir xil raqamlar bor). Shuning uchun, determinantning qiymati:

\[
\Delta = 0
\]

Determinantning qiymati 0 ga teng.

Sizga qo'shimcha ma'lumot kerakmi yoki boshqa savollaringiz bormi?

Mana, mavzuga oid beshta savol:

1. Qanday hollarda determinantning qiymati 0 ga teng bo'ladi?
2. Determinantdagi elementlarning tengligi qanday ta'sir qiladi?
3. Matritsaning determinantini hisoblashda qaysi ustun yoki qatorni tanlash yaxshiroq?
4. 4x4 matritsaning determinantini qanday hisoblash mumkin?
5. Determinantning ko'paytma va yig'indiga bo'linishi qanday hollarda qo'llaniladi?

**Maslahat:** Agar determinantda bir xil qator yoki ustunlar mavjud bo'lsa, hisob-kitoblarni davom ettirishdan oldin determinant qiymatining nolga teng ekanligini tekshiring.

Learn how to calculate the determinant of a 4x4 matrix with detailed steps and explanations. Understand when the determinant value equals zero and its implications. Suitable for advanced high school students and learners interested in matrix algebra.

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