https://file.aiquickdraw.com/mathbot/file/1727020636427vze3rftz.jpg

The matrix in the image is:

\[
\begin{bmatrix}
1 & 1 & 1 & 4 \\
1 & -1 & 2 & 3 \\
2 & 3 & -1 & 6
\end{bmatrix}
\]

This appears to be a system of equations written in augmented matrix form. To solve this, we can use methods such as **Gaussian elimination** or **Gauss-Jordan elimination**. I'll proceed with the Gaussian elimination to convert the matrix to row echelon form, and then back-substitute to find the solution.

Let me perform the steps to solve this.The augmented matrix has been reduced to:

\[
\begin{bmatrix}
1 & 1 & 1 & 4 \\
0 & 1 & -0.5 & 0.5 \\
0 & 0 & 1 & 1
\end{bmatrix}
\]

From this, we can back-substitute and find the solution to the system of equations:

\[
x_1 = 2, \quad x_2 = 1, \quad x_3 = 1
\]

This means the solution to the system is:

\[
x_1 = 2, \quad x_2 = 1, \quad x_3 = 1
\]

Would you like more details on the steps involved? Here are some related questions:

1. How does Gaussian elimination work?
2. What is the purpose of row reduction in solving a matrix?
3. Can this system be solved using other methods like Cramer's rule?
4. How does back substitution work in a system of equations?
5. What are the applications of solving systems of equations in real life?

**Tip:** Gaussian elimination is a systematic method to solve systems of linear equations by transforming the system into upper triangular form.

Solve the matrix system shown in the image.

This page explains how to solve a system of equations represented as an augmented matrix using Gaussian elimination. The solution involves reducing the matrix to row echelon form and applying back substitution. Learn how to find the solution for variables x₁, x₂, and x₃ with step-by-step explanations.

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