How do I solve this question, I don't understand.

Question

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 – z = -1. Perform row operations on your system to obtain a row-echelon form and the solution. 

Go to the 3D calculator website (GeoGebra: geogebra.org/3d?lang=pt) and enter each of the equations. 

After you have completed this first task, choose one of the following to complete your assignment:

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 = z 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.

Help me detailed explanation and calculation.

Answer 1

In a matrix row-echelon form means the main diagonal is all 1's and the elements below the main diagonal are all 0, in other words a (upper) triangular matrix with all 1's on the main diagonal.

In this form it is a relatively easy job to "solve" the simultaneous set of equations represented by the matrix equation.

Getting the matrix into this form can be done in the way you may have previously called "elimination".

Start out by dividing each row (and the constant) by first element of each row as long as it is not 0 (if it is 0 leave it alone).

Subtract the first row from each of the other 2 rows so that the first element in each row except the first is 0.

The proceed in a similar fashion with the rows: divide by the first element and subtract the 2nd row from the third. This should give you row-echelon form.

I cannot help you with GeoGebra...sorry!