Question

The input-output relationship of a linear system is given by _______.

• A. $y = a_0 x^2 + a_1 x + a_0$
• B. $y = a_1 x^2 + a_0$
• C. $y = a_1 x_1 + a_2 x_2$
• D. $y = a_0$

Hint:

Check for powers and cross-products in expressions. If present, the system is nonlinear.

Answer 1

The Correct Option is C

Step 1: Understand linearity.
A system is linear if:
- It obeys superposition
- Output is a weighted sum of inputs
Step 2: Analyze the options.
Option (3) is linear because: \[ y = a_1 x_1 + a_2 x_2 \] is a linear combination of multiple input variables.
Options (1) and (2) contain nonlinear terms like $x^2$, which violate linearity.
Conclusion: $\boxed{y = a_1 x_1 + a_2 x_2}$ is the only linear expression.