MAT 213 Final: Final Exam Study Guide Notes

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plummoose320

20 Jan 2018

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Provide a generalization to each of the key terms listed in this section. The three dimensional coordinate system consists of 3 coordinates axes (hence why 2d coordinate systems only have 2 axes), which are the following: 3d x axis y axis z axis. Since 2d planes only have 2 points to deal with (aka x and y), it is split into 4 regions called quadrants since 22 = 2 2 = 4; that is the same concept with 3d planes. Since the three dimensional coordinate system has 3 coordinates axes, then it also has 3 planes as well. Since there are 3 coordinates axes and 3 planes (while all connected by o, which is the origin), then it means that there are also 3 equations for each of their respective coordinate planes. The following is a respective connection between the equations and their respective coordinate planes:

Related Questions

First, create 3 equations of the form ax+by+cz=d , where a, b, c, and d are constants (integers between – 5 and 5). For example, x + 2y – 2= -1 . Perform row operations on your system to obtain a row-echelon form and the solution. Go to the 3D calculator website GeoGebra and enter each of the equations. After you have completed this first task, choose one of the following to complete your discussion post. 1. Reflect on what the graphs are suggesting for one equation, two equations, and three equations, and describe your observations. Think about the equation as a function f of x and y, for example, x + 2y +1 = 2 in the example above. Geogebra automatically interprets this way, that is, like z=f(x, y)=x+2y+1 , it isolates z in the equation. 2. What did the graphs show when you entered the second equation? 3. Give a simple description of the system x=0 y=0 z=0 x = 0 can be seen as the constant function x=g(y, z)=0y+0z=0 . Of course, you can use GeoGebra to “observe” the system. 4. Give an example with 2 equations as simple as possible with 3 variables (at least 1 being non-linear; keeping z to the one power on both equations) and describe the potential of GeoGebra to study nonlinear systems.

purpledonkey271

First, create 3 equations of the form $ax+by+cz=d$ , where a, b, c, and d are constants (integers between – 5 and 5). For example, $x + 2y – 2= -1$ . Perform row operations on your system to obtain a row-echelon form and the solution.

Go to the 3D calculator website GeoGebra and enter each of the equations.

After you have completed this first task, choose one of the following to complete your discussion post.

1. Reflect on what the graphs are suggesting for one equation, two equations, and three equations, and describe your observations. Think about the equation as a function $f$ of x and y, for example, $x + 2y +1 = 2$ in the example above. Geogebra automatically interprets this way, that is, like $z=f(x, y)=x+2y+1$ , it isolates z in the equation.

2. What did the graphs show when you entered the second equation?

3. Give a simple description of the system

x=0
y=0
z=0

x = 0 can be seen as the constant function $x=g(y, z)=0y+0z=0$ . Of course, you can use GeoGebra to “observe” the system.

4. Give an example with 2 equations as simple as possible with 3 variables (at least 1 being non-linear; keeping z to the one power on both equations) and describe the potential of GeoGebra to study nonlinear systems.

purpledonkey271

MAT 213 Final: Final Exam Study Guide Notes

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