It seems that you've uploaded a document with a linear system problem. Let's break down each of the tasks you need help with:

1. Solving the Linear System using Gauss-Jordan Elimination: The system you provided is: $3x - y + z = 4$ $x + 2y - z = 2$ $5x + 2y - 2z = 3$ I will use the Gauss-Jordan elimination method to solve this system.

2. Finding the inverse of matrix A: You provided the system of equations, which can be written in matrix form as: $A \cdot x = b$ Where:

   b = \begin{bmatrix} 4 \\ 2 \\ 3 \end{bmatrix}$$ You are asked to find the inverse of the matrix $$A$$ and use it to solve for $$x$$, which can be computed using: $$x = A^{-1} \cdot b$$

3. Solving another system of equations: The second set of equations is: $x_1 + 2x_2 + 3x_3 + 4x_4 = 5$ $4x_1 + 3x_2 + 2x_3 + x_4 = 0$ $3x_1 + 2x_2 + x_3 + 4x_4 = -1$ $2x_1 + x_2 + 3x_3 + 4x_4 = 4$ You are also asked to solve this linear system.

Let me solve each part step by step. Would you like me to start with the Gauss-Jordan elimination for the first system, or is there a specific part you'd prefer to focus on first?