LinearSystemsSolver solves systems of linear equations with 2 to 23 (inclusive) equations and 2 to 23 (inclusive) variables. It uses the Gauss-Jordan elimination method and several conditioning techniques to effectively resolve unique solutions, parametric solutions and inconsistency.
The user is provided with a keypad, a two-line text field for input, a help window briefly describing the app’s operation and a solution box where warnings (in red), messages and solutions appear. Solutions are given in both fractional and decimal form.
The text field and keypad allow the editing of single characters without a touch feature. Scrolling keys Left and Right are fast if held down. The Up and Down keys allow the user to easily switch lines to quickly edit inputs. To edit an entry, use the Left, Right, Up or Down keys to place the cursor to its right, then either add a character, delete the character using Del or replace it.
A scrollable second window for big solutions can be accessed at the press of a button.
To solve systems of linear equations enter the number of equations (an integer between 2 and 23 inclusive) then a comma, then enter the number of variables (an integer between 2 and 23 inclusive) then a comma. Enter the coefficients of each equation and their righthand constants in order of appearance from left to right; separate each coefficient, righhand constant and equation with a comma. End with a comma. Press Solve. For example, to solve the system 3a+5b=1, -2a-11b=7, 5a+4b=6, enter the number of equations, 3, the number of variables, 2, or 3,2, followed by the coefficients and constants 3,5,1,-2,-11,7,5,4,6, (note the commas and the position of the righthand constants 1, 7 and 6). The textfield should read as 3,2,3,5,1,-2,-11,7,5,4,6, . Pressing Solve now gives the fractional solution a=2, b=-1 and the equivalent decimal solution a=2.0, b=-1.0.
To solve the system 4a+3b=1, -2a-9b=2, we enter 2,2,4,3,1,-2,-9,2 in the textfield. After pressing Solve, we get the fractional solution a=1/2, b=-1/3 and the equivalent decimal solution a=0.5, b=-0.3333333333333333.
Press the Clear button to edit the number of equations or variables, to solve another system or when exiting the app. Press or hold the right or left arrows or Del only to edit coefficients and constants. Write 9. as 9.0. Write 10,000 as 10000.
Press More space if the solution is too large for the solution box.
"To solve a linear programming problem (LP),enter the objective function P by tapping the box below A; enter a number using the number pad. Repeat this using the box below B. Tap P, then Input. Enter constraints:numbers below A,below B and below C, respectively. Tap the red box then tap Reset,Input, Graph, Graph1 (the red graph). Repeat these steps for each constraint using Reset, a different colored box and Graph for each constraint. Find corner points by tapping Solve, Solve1, Solve2 etc. P-values at corner points are below P in order of Solve output. The solution appears in one of the boxes below P. To edit a coefficient of a graphed constraint, tap its color-box, Clear. Tap Graph1, Graph2 etc in that order. Do not tap the Graph button for the constraint you are editing. Tap the box you want to edit and enter the correction; then tap, Reset, tap the colored box whose constraint you wish to correct and tap input and graph, then tap its Graph button you left out before. "
LinearSystemsSolver 1.5.9 Update
2023-06-06
LinearSystemsSolver handles solving systems of simultaneous linear equations, this version of the app also solves linear programming problems (maximization) in two nonnegative variables with up to four constraints. It uses the graphical method. Tapping the LP-button brings the user to the linear programming interface. It provides the means of inputting the objective function and the constraints. It graphs the boundary for the feasibility region (which is optional), determines the intersection points and decides which intersection points are feasible (or corner points). Lastly, it evaluates the objective function at each corner point. The results are in boxes that correspond to the corner points. From this, a user can select the optimal solution. This should be easy to carry out. The 0.0 and 7.0 buttons have been repaired and now operate much better than in previous versions. The reset button, that we refer to in the previous description, has been added. It allows the user to graph vertical lines and prevents coefficients in different constraints from mixing. The user must tap the reset button then a coloured box to input a constraint.
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LinearSystemsSolver handles solving systems of simultaneous linear equations, this version of the app also solves linear programming problems (maximization) in two nonnegative variables with up to four constraints. It uses the graphical method. Tapping the LP-button brings the user to the linear programming interface. It provides the means of inputting the objective function and the constraints. It graphs the boundary for the feasibility region (which is optional), determines the intersection points and decides which intersection points are feasible (or corner points). Lastly, it evaluates the objective function at each corner point. The results are in boxes that correspond to the corner points. From this, a user can select the optimal solution. This should be easy to carry out. The 0.0 and 7.0 buttons have been repaired and now operate much better than in previous versions. The reset button, that we refer to in the previous description, has been added. It allows the user to graph vertical lines and prevents coefficients in different constraints from mixing. The user must tap the reset button then a coloured box to input a constraint.
1.3.7
2023-02-08
The app now allows dimensions of 23 equations in 23 variables. A few bugs have been corrected.
1.3.2
2020-04-02
This version of LinearSystemsSolver enhances input capability by providing a two-line textfield. This makes it easier for users to detect and correct errors without scrolling, at least for smaller systems such as those with four or fewer equations with four or fewer variables. Left and Right cursor movement is still available but Up and Down keys have been added so users can quickly change lines. Rows of text still scroll left or right by either overfilling the textfield at the left or right end of the field, or by moving the cursor to the left end on the first line, or to the right end on the second line.