Solve f3=(1/3)f1+f3

$$f 3 = ( \frac { 1 } { 3 } ) f 1 + f 3$$

Solve for f_1

$$f_{1}=0$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{3}f_{1}+f_{3}=f_{3}$$

Subtract f_{3} from both sides.

$$\frac{1}{3}f_{1}=f_{3}-f_{3}$$

Combine f_{3} and -f_{3} to get 0.

$$\frac{1}{3}f_{1}=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since \frac{1}{3} is not equal to 0, f_{1} must be equal to 0.

$$f_{1}=0$$

Solve for f_3 (complex solution)

$$f_{3}\in \mathrm{C}$$

$$f_{1}=0$$

Solve for f_3

$$f_{3}\in \mathrm{R}$$

$$f_{1}=0$$