MATH 1021 Lecture : Section 12 1 Class Notes

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azuremammoth471

15 Mar 2019

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Document Summary

Objective 1 verifying solutions to a system of linear equations in two variables. A linear equation in one variable is as an equation that can be written in the form ax+b=0 where a and b are real numbers with. A linear equation in n variables is an equation that can be written in the form a x. This definition can be extended to more variables as follows: ,n x and real numbers 1 n a a. 2, x x a is nonzero. n where at least one of 1. = is a linear equation in two variables while. 11 is a linear equation in three variables. The important thing to remember is that all variables of a linear equation have an exponent of 1. A system of linear equations in two variables. A system of linear equations in two variables is the collection of two linear equations considered simultaneously.

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

I have the answer for the following question. But some of theanswers are not correct.

Please do the following question by yourself and check which arethe wrong answers,please post your answers and compare to it.