https://file.aiquickdraw.com/mathbot/file/1724675148149yjuuk8cd.jpg

Quyidagi determinant qiymati nimaga teng?

Keltirilgan determinantning qiymatini topish uchun ushbu determinantni hisoblaymiz. Determinant quyidagicha ko'rinishda:

\[
\Delta = \begin{vmatrix} -4 & 3 & 12 \\ -5 & 6 & 0 \\ 2 & -1 & 0 \end{vmatrix}
\]

Bu determinantni hisoblash uchun, birinchi qatordan foydalanib, kichik determinantlar yordamida ochamiz:

\[
\Delta = -4 \cdot \begin{vmatrix} 6 & 0 \\ -1 & 0 \end{vmatrix} - 3 \cdot \begin{vmatrix} -5 & 0 \\ 2 & 0 \end{vmatrix} + 12 \cdot \begin{vmatrix} -5 & 6 \\ 2 & -1 \end{vmatrix}
\]

Endi har bir 2x2 kichik determinantni hisoblaymiz:

1. \(\begin{vmatrix} 6 & 0 \\ -1 & 0 \end{vmatrix} = (6 \cdot 0) - (0 \cdot -1) = 0\)
2. \(\begin{vmatrix} -5 & 0 \\ 2 & 0 \end{vmatrix} = (-5 \cdot 0) - (0 \cdot 2) = 0\)
3. \(\begin{vmatrix} -5 & 6 \\ 2 & -1 \end{vmatrix} = (-5 \cdot -1) - (6 \cdot 2) = 5 - 12 = -7\)

Endi bu qiymatlarni asosiy formulaga qo'yamiz:

\[
\Delta = -4 \cdot 0 - 3 \cdot 0 + 12 \cdot (-7) = 0 + 0 - 84 = -84
\]

Shunday qilib, determinantning qiymati \(\Delta = -84\) ga teng.

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

Mana, mavzuga oid beshta savol:

1. 2x2 determinantni qanday hisoblash mumkin?
2. Determinantning geometrik ma'nosi nima?
3. Uchburchak shaklidagi determinantning qiymati qanday hisoblanadi?
4. Determinantning qanday asosiy xususiyatlari mavjud?
5. Nima uchun determinant qiymati noldan farqli bo'lsa, matritsa o'ziga xos bo'ladi?

**Maslahat:** Matritsa determinantini hisoblashda biror bir qator yoki ustundagi eng ko'p nollarni o'z ichiga olgan satr yoki ustunni tanlash, hisob-kitoblarni soddalashtiradi.

Learn how to calculate the determinant of a 3x3 matrix step-by-step with detailed examples. This problem covers key concepts in matrix algebra and determinant properties. Suitable for advanced high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation