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Here is all you need to know about Linear Systems

Do you know a linear equation is an equation that includes two variables? And a linear equation is a combination of two variables and a constant.

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Top things to learn about Linear Systems from the online tutor:
 

  • Understanding linear system 
  • Understanding linear equations 
  • Understanding linear equation graph 
  • Simultaneous linear equations 
  • Two variable linear equations 
     
  1. ​​Simple linear systems
     
  • Homogeneity
  • Superposition
  • Additivity
     
  1. Shift-invariance
     

  • Decomposing a signal into a set of shifted and scaled impulses
  • Characterizing a shift-invariant system using sinusoids
  • Use of sinusoids in analyzing shift-invariant linear systems
  • The impulse response function
  • Decomposing stimuli into sinusoids via Fourier Series
     
  1. Examples
     

  • Stereo
  • Swinging pendulum

 

Linear Systems Frequently Asked Questions

Question 1: How to solve systems of linear equations?
Generally, an easy way to solve the system of linear equations is by using substitution. For example, if we have two linear equations with two variables. By substituting the value of one variable to another equation, we will be getting an equation with one variable.

And, we can isolate the variable from the equation with one variable. Later, we can plug this solution into any one of the given equations and solve for another variable.

 

Question 2: How to solve systems of linear equations by graphing?
To solve the system of linear equations using graphs, we need to plot the given equations on the same coordinate plane.

If the graph of the equation intersects each other at some point, we can say these systems of the linear equation has a unique solution. And, if their graphs did not intersect each other at any point, we can conclude that this system of linear equations has no solution.

And, if their graph superimposes each other, then they will have an infinite number of solutions.

 

Question 3: How to solve systems of linear inequalities?
Linear inequalities can be solved with methods that we use in solving systems of linear equations. The main difference is that, in linear inequalities, we do not solve for a point. Instead, we solve for a region that satisfies the given inequalities.

The most common way to a system of linear inequalities is by using the graph. Here, we will treat the linear inequalities as a linear equation and plot their graph. And, we need to identify and shade the region that satisfies the given linear inequalities.

 

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