91Ó°ÊÓ

First, let's represent the given system of equations in the form of an augmented matrix: $$ \left[\begin{array}{cc|c} 2 & 3 & 2 \\ -1 & -\frac{3}{2} & -\frac{1}{2} \end{array}\right] $$

Now, we will perform row reductions by following these steps: 1. Make the element (1,1) equal to 1 (pivot). 2. Make the elements below the pivot equal to 0. 3. Move to the next diagonal element (2,2) and make it equal to 1 (pivot). 4. Make the elements above the pivot equal to 0. First, we'll make element (1,1) equal to 1 by dividing the first row by 2: $$ \left[\begin{array}{cc|c} 1 & \frac{3}{2} & 1 \\ -1 & -\frac{3}{2} & -\frac{1}{2} \end{array}\right] $$ Next, we'll make the element (2,1) equal to 0 by adding the first row to the second row: $$ \left[\begin{array}{cc|c} 1 & \frac{3}{2} & 1 \\ 0 & 0 & \frac{1}{2} \end{array}\right] $$ At this point, the row reduction procedure reveals that the second equation is invalid \(0 \neq \frac{1}{2}\), therefore the system of equations has no solution. The result is an inconsistent system.