Q7) TRUE or FALSE:a) A system is "linear" whenever its output y(t)=A x(t) + B for some constants A and B. (TRUE or FALSE?)b) If you input a signal x₁(t) into a linear system and obtains y₁(t); then the output of the system whenyou later input a signal -4x1(t) will be -4y₁(t). (TRUE or FALSE?)c) A system is called "time invariant" if its output y(t) does not change over time; i.e. y(t) equals aconstant. (TRUE or FALSE?)d) The output of an LTI system can be written as the sum of 3 responses: the zero-input response, thezero-state response, and the zero-output response. (TRUE or FALSE?)e) Each LTI can sustain certain forms of responses on its own, without an external input, and these arecalled the characteristic modes of the system. (TRUE or FALSE?)

Answered: a) A system is "linear" whenever its…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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Q7) TRUE or FALSE:
a) A system is "linear" whenever its output y(t)=A x(t) + B for some constants A and B. (TRUE or FALSE?)
b) If you input a signal x₁(t) into a linear system and obtains y₁(t); then the output of the system when
you later input a signal -4x1(t) will be -4y₁(t). (TRUE or FALSE?)
c) A system is called "time invariant" if its output y(t) does not change over time; i.e. y(t) equals a
constant. (TRUE or FALSE?)
d) The output of an LTI system can be written as the sum of 3 responses: the zero-input response, the
zero-state response, and the zero-output response. (TRUE or FALSE?)
e) Each LTI can sustain certain forms of responses on its own, without an external input, and these are
called the characteristic modes of the system. (TRUE or FALSE?)

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Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts for you. To get the remaining sub-part solved please repost the complete question and
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Linear System:-

A linear system is a mathematical representation of a system in systems theory that relies on the application of a linear operator.
Compared to nonlinear systems, linear systems often have significantly simpler traits and properties.

Non-Linear System:-

A larger class of systems that do not adhere to the superposition principle are covered by nonlinear control theory.
Since all genuine control systems are nonlinear, it applies to more real-world systems.
In many cases, nonlinear differential equations regulate these systems.

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