Solve the given equations using Gauss Jordan method.

3x+3y+3z=9
6x-9y+12z=13
9x+12y+15z=40

Group of answer choices

x=1.67, y=1, z=0.33

x=1, y=0.33, z=1.67

x=0.33, y=1.67, z=1

x=0.33, y=1, z=1.67

To solve the system of equations using the Gauss-Jordan method, we first write the system as an augmented matrix and then perform row operations to get the matrix into reduced row-echelon form (RREF).

The given system of equations is:

\[
\begin{aligned}
1. & \ 3x + 3y + 3z = 9 \\
2. & \ 6x - 9y + 12z = 13 \\
3. & \ 9x + 12y + 15z = 40
\end{aligned}
\]

This can be written as the augmented matrix:

\[
\begin{pmatrix}
3 & 3 & 3 & 9 \\
6 & -9 & 12 & 13 \\
9 & 12 & 15 & 40
\end{pmatrix}
\]

Now, let's perform the Gauss-Jordan elimination. I'll calculate the result step by step.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you still want to go over the Gauss-Jordan method manually, I can guide you step by step on how to solve it. Would you like me to walk you through that?

Here are some follow-up questions related to the topic:
1. What are the main differences between Gaussian elimination and Gauss-Jordan elimination?
2. How do we determine when a system of linear equations has no solution using the Gauss-Jordan method?
3. What role does pivoting play in Gaussian elimination?
4. Can the Gauss-Jordan method be used for systems of equations with more than three variables?
5. How can we apply matrix inversion to solve systems of linear equations?

**Tip:** When using Gauss-Jordan elimination, always ensure that the pivot element is non-zero before proceeding with row operations.

Solve the given equations using Gauss Jordan method. 3x+3y+3z=9, 6x-9y+12z=13, 9x+12y+15z=40. Group of answer choices: x=1.67, y=1, z=0.33; x=1, y=0.33, z=1.67; x=0.33, y=1.67, z=1; x=0.33, y=1, z=1.67

Learn how to solve a system of linear equations using the Gauss-Jordan method. This example includes solving 3x+3y+3z=9, 6x-9y+12z=13, and 9x+12y+15z=40. Explore key concepts such as augmented matrices and row operations in linear algebra. Suitable for Grades 11-12 and early college students.

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