(lambdaI-A)=0 eching

$$( \lambda I - A ) = 0$$

I uchun yechish (complex solution)

$$\left\{\begin{matrix}I=\frac{A}{\lambda }\text{, }&\lambda \neq 0\\I\in \mathrm{C}\text{, }&A=0\text{ and }\lambda =0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

A ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$\lambda I=A$$

Ikki tarafini \lambda ga bo‘ling.

$$\frac{\lambda I}{\lambda }=\frac{A}{\lambda }$$

\lambda ga bo'lish \lambda ga ko'paytirishni bekor qiladi.

$$I=\frac{A}{\lambda }$$

A uchun yechish

$$A=I\lambda$$

Yechim qadamlari

Ikkala tarafdan \lambda I ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-A=-\lambda I$$

-1ni ikki tarafidan bekor qilish.

$$A=\lambda I$$

I uchun yechish

$$\left\{\begin{matrix}I=\frac{A}{\lambda }\text{, }&\lambda \neq 0\\I\in \mathrm{R}\text{, }&A=0\text{ and }\lambda =0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

A ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$\lambda I=A$$

Ikki tarafini \lambda ga bo‘ling.

$$\frac{\lambda I}{\lambda }=\frac{A}{\lambda }$$

\lambda ga bo'lish \lambda ga ko'paytirishni bekor qiladi.

$$I=\frac{A}{\lambda }$$