Question

What is a linear system?

(a) A system which follows homogeneity and additivity

(b) A system which follows additivity

(c) A system which follows homogeneity

(d) Almost every system is linear

This question was posed to me at a job interview.

My question is from Linear Systems topic in division Beyond the Basics of MATLAB

Answer 1

Right answer is (a) A system which follows homogeneity and additivity

Explanation: A system which follows homogeneity and additivity is called linear system. This comes from the definition of superposition and here is the proof:

Taking a system with which produces y1(t) as output for an input x1(t) and an output y2(t) for an input x2(t),

HOMOGENITY: For input ax1(t), output should be ay1(t) and for input bx2(t), output should be by2(t).

ADDITIVITY: For a input of sum of x1(t) and x2(t), output should be the sum of a y1(t) and y2(t), i.e. the sum of individual response

Finally, if for an input of the sum of ax1(t) and bx2(t), if we get the output as sum of ay1(t) and by2(t) the system is both homogeneous and additive. This is similar to the superposition principle. No the system is linear.