A graphical interface to solve matrices as well as other linear algebra computations
Matrix and Vector Constructors have been added, as well as Elementary row operations for Matrices
| Operation | Function |
|---|---|
| Swap | Swaps Row 1 with Row 2 |
| Scalar Multiply | Scales a Row by a constant |
| Add | Adds a scaled row to another Row |
Ref and RRef are algorithms to convert a matrix into Reduced Echelon Form, and Reduced Echelon Form, in the goal of determining numerous pieces of info about the matrix. These functions are used extensively by other sections of the project. They use several helper methods to streamline the operation.
- First determine if a row, starting with row one, has 1 one in the column.
- If no one exists, determine if a row has all values divisible by leading value, then divide all values by leading to get a one in the first column
- If no one exists and divisible, select 1st row, and divide by leading value.
- If row that was selected is not row 1, swap row with row 1
- Using the first row, subtract it from each row below it, multiplying the first row by the leading value of each row
- Repeat steps 1 - 5 using the next column, but if the column is an all zero column not including rows with pivots already, move on to the next column and mark as pivot
- Preform until all possible pivots are created, creating a Reduced Echelon Form Matrix.
Ref also sets the values in two arrays, representing the rows and columns, for use in other algorithms, as well sets the ref flag to true.
- Preform Ref on Matrix if not already done
- Using the the row, starting from the bottom, subtract off from all rows above, multiplying by the value in that column of each row
sets the RRef flag to true
Variable displays each variable, indicating if it is a free variable or showing it as the summation of free variables and the value in the augmented column. Assumes the matrix is augmented
Vector form generates vectors representing each of the free variables, as well as the constant vector, displaying it
Augments the matrix with a new column, represented by a vector
Matrix Function is an extension of matrix and is set up in the form Ax = b. A matrix is given to represent A and info about it such as onto and 1 to 1 are determined. The function can also display is a b is in the range, give a potential input for b, and generate the output for x
The system form is one of the gui screens available to the user, and is used to solve a system equation. It preforms as follows:
Reads in a system of a equations, using two parameters, # of Variables, and # of Equations.
The variables are allowed are X1 .... X(# of variables), in any order. Each variable must be separated by " + " and the equation must be in the form X1 + 5X2 + 6X3 = 5 for example, with each opeator and variable separated by a space.
Vector or variable form is specified, and if properly inputed, the answer will be pumped out
Matrix is the simplest of gui tabs, simply specify the number of columns and rows for the matrix. press generate, and the matrix will be created. Fill with values of your choice, and use the functions listed to manipulate the matrix.
Uses the matrix function class and part of the Matrix gui. Specify the rows and columns for A, then press generate. It will generate A as well as the acceptable X vector and the vector b that will generated. Fill A with the desired function and press generate function, which will set the onto and 1 to 1 flags based on the matrix. The three buttons preform as specified by filling out the necessary vector, the output of the button will be placed in the necessary vector