User manual TERRAILLON TFA NAUTIC

[. . . ] TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 2 What Is the Polynomial Root Finder & Simultaneous Equation Solver Application? The Polynomial Root Finder application calculates the roots (zeros) of polynomials of degree 1 through 30, with a convenient, easy to use interface. You can store solutions into lists, load lists into the application for editing, and graph the polynomial. Because the application uses the operating system’s eigenvalue routines, solutions are computed numerically only. The Simultaneous Equation Solver application finds solutions to systems of linear equations. [. . . ] Press ¯ after each entry. Tip You can press ` or h to move the cursor to an entry to change it. TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 27 7. Enter the coefficients for the variables and the constants in the matrix: 1 M 500000   1 1 . 09 . 1 . 12 M 52000    2. 5 - 1 0 M 0    This matrix shows the values in Float mode. 8. You see that the corporation borrowed $100, 000 at 9%, $250, 000 at 10%, and $150, 000 at 12%. TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 28 Now that you have completed the Getting Started example, you can read further for more detailed instructions on how to use the Simultaneous Equation Solver application. Some topics you might want to explore are • Loading a matrix into the application • Storing data to a matrix • Displaying a matrix in reduced row-echelon form TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 29 Starting and Quitting the Simultaneous Equation Solver Application Starting the Application 1. Select Quit PolySmlt. Shortcut You can also press \  to exit the application. If the cursor is at a name prompt, you must press \  twice. TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 30 Selecting Simultaneous Equation Solver Options Several options are that you can use to accomplish specific tasks displayed across the bottom of each screen. To select an option, press the graphing key directly under the option. Press a graphing key to select one of these options. RSTUV Options You Can Use Use options on this screen … To do this: MAIN displays the main menu. LOAD displays a prompt so that you can enter a matrix name that contains the matrix values you want to use. You must set up the matrix in the matrix editor before you can use it in the Simultaneous Equation Solver application. You cannot access the matrix editor while the application is running. Equations/unknowns entry screen TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 31 Use options on this screen … To do this: MAIN displays the main menu. NEW displays the equations/unknowns entry screen where you can view or change the number of equations and number of unknowns. SYSMATRIX screen CLR clears all of the matrix values that you have entered. If you select this mode setting and the answer is complex, NONREAL is displayed as the result. a+bi (rectangular complex) mode displays complex numbers in the form a+bi. 6 re^6i (polar complex) mode displays complex numbers in the form of re Ti. 4. Select ESC to save the settings and return to the previous screen. TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 37 Entering and Solving a Problem To solve a system of equations, you enter the number of equations, the number of unknowns, and then you enter the augmented matrix (one that contains the coefficients as well as the constants) of the system. Note The Simultaneous Equation Solver application does not find solutions to complex systems. The augmented matrix can only contain real numbers. The following example solves this system of equations: x+ y+ z=5 2x 1 . 5y + z = 10 x 1 2y + 3z = 15 1. Enter the number of equations (3) and the number of unknowns (3), pressing ¯ after each entry. TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 38 2. Press ¯ after each entry to move to the next value. Tip You can use `, h, a, and _ to scroll through the list of coefficients and constants to edit values, if necessary. 3. This may take several seconds. TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 39 Loading a Matrix You can load an augmented matrix from the equations/unknowns entry screen or the SYSMATRIX screen. You must set up the matrix in the matrix editor before you can use it in the Simultaneous Equation Solver application. The size of the matrix must be appropriate for the number of equations and number of unknowns. For example, if you enter 5 as the number of equations and 3 as the number of unknowns, the matrix must be 5x4. [. . . ] 5 Polynomial Root Finder Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Getting Started with the Polynomial Root Finder Application. . . . . . . . . . . . . . . . . . . . 6 Starting and Quitting the Polynomial Root Finder Application. . . . . . . . . . . . . . . . . 13 Selecting Polynomial Root Finder Options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [. . . ]