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It appears that you have uploaded two images containing mathematical content. I will examine the images to identify the equations and problems provided, and then I'll solve them. Let me start by analyzing the content.Upon analyzing the images, it seems you have a system of linear equations represented by a matrix, and the problem involves solving for the vector \(\vec{x}\) using matrix methods.

The first matrix representation is:
\[
\begin{bmatrix}
2 & -3 & -5 \\
1 & 2 & 1 \\
3 & 1 & 2 
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2 \\
x_3 
\end{bmatrix}
=
\begin{bmatrix}
7 \\
4 \\
5 
\end{bmatrix}
\]

The equation represented here is \(\mathbf{A}\vec{x} = \vec{b}\), where \(\mathbf{A}\) is the coefficient matrix, \(\vec{x}\) is the column vector of unknowns, and \(\vec{b}\) is the result vector.

I'll solve this system using the matrix inversion method.

Given:
\[
\mathbf{A} = \begin{bmatrix} 2 & -3 & -5 \\ 1 & 2 & 1 \\ 3 & 1 & 2 \end{bmatrix}, \quad \vec{b} = \begin{bmatrix} 7 \\ 4 \\ 5 \end{bmatrix}
\]

The solution to \(\vec{x}\) can be found by calculating:
\[
\vec{x} = \mathbf{A}^{-1} \cdot \vec{b}
\]

Let's proceed to solve this step by step.

Learn how to solve a system of linear equations using matrix methods with step-by-step instructions. This problem involves matrix operations including multiplication and inversion. Suitable for college-level students studying linear algebra.

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