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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: www.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 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=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.

Sagot :

Jellyy2539

Answer:

The solution is x=0, y=0, z=1

Step-by-step explanation:

Step1:   -row2 + row1;  -row2 + row3

x + 2y - z = -1

 x  + y  + z = 1

 x - y  - z  = -1

 1   2   -1    -1

 1   1    1     1

 1  -1    -1   -1

0  1  -2  -2

1  1   1   1

0 -2  -2  -2

Step 2: row3/-2

0   1   -2    -2

1   1    1     1

0   1    1     1

step 3:  -row3 + row1

0   0   -3    -3

1   1    1     1

0   1    1     1

step 4:  row1/-3

0   0    1     1

1   1    1     1

0   1    1     1

step 4: -row1 + row3; -row1 + row2

0   0    1     1

1   1    0     0

0   1    0     0

step 5:  -row3 + row2

0    0    1    1

1    0    0    0

0    1    0    0

The reduced row echelon form is:

1    0    0     0

0    1    0     0

0    0    1     1

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