Solve C-lambdaI=0

$$C - \lambda I = 0$$

Solve for I

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

Steps for Solving Linear Equation

Subtract C from both sides. Anything subtracted from zero gives its negation.

$$-\lambda I=-C$$

Cancel out -1 on both sides.

$$\lambda I=C$$

Divide both sides by \lambda .

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

Dividing by \lambda undoes the multiplication by \lambda .

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

Solve for C

$$C=I\lambda$$

Solution Steps

Add \lambda I to both sides. Anything plus zero gives itself.

$$C=\lambda I$$