Can you confirm rough answer is correct? Is there anything I should add from the source material?

QUESTION:

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.

Use this source material: https://openstax.org/books/algebra-and-trigonometry-2e/pages/11-6-solving-systems-with-gaussian-elimination

ROUGH ANSWER/NOTES:

Quote from chapter 11.6

Notice that the matrix is written so that the variables line up in their own columns: x-terms go in the first column, y-terms in the second column, and z-terms in the third column. It is very important that each equation is written in standard form ax+by+cz=d so that the variables line up. When there is a missing variable term in an equation, the coefficient is 0.

Equation one: 2x + 3y - 4z = -5

Coefficient of x: 2

Coefficient of y: 3

Coefficient of z: -4

Right-hand side: -5

Equation Two: -x + 5y + 2z = 3

Coefficient of x: -1

Coefficient of y: 5

Coefficient of z: 2

Right-hand side: 3

Equation Three: 4x - 2y + 3z = 7

Coefficient of x: 4

Coefficient of y: -2

Coefficient of z: 3

Right-hand side: 7

To solve this system using Gaussian elimination. TheGaussian elimination is a method that utilizes row operations to achieve row-echelon form.

Step one is to write the augmented matrix.The augmented matrix displays the coefficients of the variables, and an additional column for the constants. "When there is a missing variable term in an equation, the coefficient is 0."

[2 3 -4 -5]

[-1 5 2 3]

[4 -2 3 7]

Then we perform the following row operations to obtain the row-echelon form. "Row-echelon form is which there are ones down the main diagonal from the upper left corner to the lower right corner, and zeros in every position below the main diagonal"

To obtain the row-echelon form, where there are ones along the main diagonal from the upper left corner to the lower right corner and zeros below the main diagonal, we can perform the following row operations:

1.Interchange rows: We can swap the positions of two rows (Ri Rj).

2.Multiply a row by a constant: We can multiply all elements of a row by a nonzero constant (cRi).

3.Add the product of a row multiplied by a constant to another row: We can multiply a row by a constant, and then add it to another row (Ri + cRj).

1.R2 + 2R1 R2

[2 3 -4 -5]

[0 11 -6 -7]

[0 -8 11 17]

2. R3 - 2R1 R3

[2 3 -4 -5]

[0 11 -6 -7]

[0 0 (11/11) (17/11)]

Finally, the matrix is in row-echelon form,

Now we can easily solve for z, y, and x:

z = 17/11

y = (6/11)z - (7/11) = 5/11

x = (4/11)z + (3/11) = 7/11

So the solution to the system of equations is (x, y, z) = (7/11, 5/11, 17/11).

Can you show me a screen shot of these graphs? from here? www.geogebra.org/3d?lang=pt