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It is required to design a GUI tool that accepts a system of linear equations of 2, 3, or 4 variables and is capable of performing basic linear algebraic operations. The following guidelines should be followed in implementing the tool:
The user selects the number of variables in the system through a pop-up menu. Based on this number, the appropriate number of edit-text boxes are displayed. For example, for a system of two variables, six boxes are displayed. These boxes will be used to enter the coefficients of the variables and the right-hand side values of the equations.
The edit-text boxes can be populated manually by the user or by selecting a CSV file that contains the coefficients of the system. If a file is used, the tool should determine if the selected number of variables through the pop-up menu corresponds to the number of variables for the linear system contained in the file. In case of mismatch, the tool should automatically update the number of edit-text boxes and the selected number of variables in the pop-menu to match the content of the file. The CSV file is structured such that each line represents an equations and has (n+1) values, where n is the number of variables, with last number in the line being the value on the right-hand side of the equation.
After the system is defined using the edit boxes, another pop-up menu is used to select the operation to be performed on the linear system in hand. Possible operations are: finding the determinant, finding the transpose of the coefficients array, computing the inverse of the coefficients matrix that represents the equations, or to solve the linear system. Processing is started by hitting a pushbutton.
The result of each operation is displayed such that:
The determinant is displayed in a static text label.
The transpose of the coefficient array is displayed in the edit-text boxes that were used to define the system.
The inverse of the coefficient matrix is displayed in the edit-text boxes that were used to define the system. If the matrix is singular, i.e. it has no inverse; an error message should be displayed.
The solution of the system is displayed using static-text labels (a separate label is used for each variable). If the system has no solution, an error message is displayed.
When the tool is started it should be initialized to the 2-variable linear system
X + 2Y = 5
X-Y = -1
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