Lewis Reeves
ELEC 2120 Signals & Systems
9/24/2024
Lab 3: Matlab Symbolic Math Toolbox
Introduction:
This experiment introduces how to solve a system of equations in Matlab. The introduces the concept of declaring symbols in Matlab in order to find the simplified solution to an equation. The experiment shows how to graph equations and how to solve the equations using the graphs.
Procedure:
1. What are the two solutions of the second order equation: 𝑥^2 – 7𝑥 + 6 = 0.
– The solutions are x = 1 and x = 6
2. What is the solution of the system of equations: 2𝑥 + 𝑦 – 2𝑧 = 3, 2𝑥 – 𝑦 – 2𝑧 = 0, 𝑥 + 𝑦 + 3𝑧 = 12.
– The solution is x = 51/16, y = 3/2, and z = 39/16.
3. What are the centers of the two circles with radius 𝑟 = 6 and pass through the points 𝑃1 = (4,1) and 𝑃2 = (6,1)?
– The centers are (5,-4.916) and (5,6.916)
4. Solve the equation cos(𝑥) = 𝑥^2 – 6 using the graphical and the numerical approaches in example 2.3.
– The solutions are x = -2.3082 and x = 2.3082.
5. How many solutions does cos(𝑥) = sin (𝑥) have? Find the first three solutions after x = 0.
– The equation has infinite solutions. The first three are x1 = 0.7854, x2 = 3.927, and x3 = 7.069.
6. What is the solution to the equation with two solutions: x^2 – 1 = 0.5x
– The solutions are x = -0.7808 and x = 1.2808
Conclusions:
This lab introduced the concepts of solving equations using the symbols commands and graphing in Matlab.
I enjoyed learning more about solving equations with more than one method. What didn’t go well was I kept making small errors in my code that made it take longer to finish. How I would improve the lab is I would have more examples for the harder methods of solving with updated images of code.