User manual ARIANE MIX 33 SCHEMA

[. . . ] See the terms of the license agreement. Copyright © 1999, 2001 Texas Instruments Incorporated. Matrices for the MIX 33 Page 2 Where to Find Installation Instructions You can find detailed instructions on installing Flash applications at education. ti. com/guides. Matrices for the MIX 33 Page 3 Getting Started: Systems of Linear Equations Use the Matrices application to solve the system of linear equations: X + 2Y + 3Z = 3 2X + 3Y + 4Z = 3 Enter the coefficients as elements in a matrix, and then use rref( to find the reduced row-echelon form. Steps Keystrokes 9, highlight MATRICES and press b, then press any key Display 1. Display the MATRIX EDT menu, and select the [A] matrix. ""1 Matrices for the MIX 33 Page 4 Steps Keystrokes 2b 4b Display 3. The rectangular cursor indicates the current element. Ellipses (. . . ) indicate additional columns beyond the screen. [. . . ] In most cases, however, you can perform the operations successfully by breaking them into separate pieces. For example: An error occurs for: Instead, enter: [ [1, 2] [3, 4] ] + [ [5, 6] [7, 8] ] [ [1, 2] [3, 4] ] Ü [A] [ [5, 6] [7, 8] ] Ü [B] [A] +[B] [ [1, 2] [3, 4] ] Ü [A] [ [5, 6] [7, 8] ] Ü [B] augment( [A] , [B] ) identity(3) Ü [A] randM(3, 3) Ü [B] [A] * [B] augment([ [1, 2] [3, 4] ] , [ [5, 6] [7, 8] ]) identity(3) * randM(3, 3) Note These expressions cause an error because they contain three matrix operations (two input matrices and one result matrix). Matrices for the MIX 33 Page 18 Typing a Matrix Directly from the Keyboard On the Matrix Home screen, use the syntax: [ [element1, 1, . . . , element1, n], . . . , [elementm, 1, . . . , elementm, n] ] Use [ (press &) to begin the matrix. Use [ ] to enclose the elements for each row. Note: At the start, [ [ begins the matrix and then begins the first row. Note: The closing ] ] are not necessary at the end of an expression or preceding Ü (X). Any expressions are evaluated when you press b. For example: The commas that you must enter to separate elements are not displayed on output. To store a matrix directly to a matrix variable, use X. For example: Select the matrix from the Matrix NAME menu or type it directly. Press & and ' to type [ and ]. Matrices for the MIX 33 Page 19 Accessing a Specified Matrix Element On the Matrix Home screen, you can store a value to, or recall a value from, a specified matrix element. The element must be within the defined matrix dimensions. Use the syntax: [matrix] (row, column) Matrices for the MIX 33 Page 20 Displaying and Copying Matrices on the Matrix Home Screen Displaying a Matrix To display the contents of a matrix on the Matrix Home screen, select the matrix from the MATRIX NAME menu and then press b. If the matrix is too large to be displayed on the screen, press ", !, #, and $ to scroll the matrix. # or $ in the right column indicates additional rows. Ellipses (. . . ) in the left or right column indicate additional columns. Matrices for the MIX 33 Page 21 Copying One Matrix to Another To copy a matrix: 1. Each element is the cumulative sum of the column from top to bottom. cumSum(matrixname) 2, 2+4, 2+4+6 1, 1+3, 1+3+5 Note About Row Operations menu items A through F, as described in the remaining part of this section, are row operations. You can use a row operation in an expression. Row operations do not change the matrix in memory. You can enter all row numbers and values as expressions. You can select the matrix from the MATRIX NAME menu. MATRIX MTH Matrices for the MIX 33 Page 37 ref(, rref( A: and B: Row-echelon and Reduced Row-echelon Forms ref( returns the row-echelon form of a real matrixname. The number of columns must be greater than or equal to the number of rows. ref(matrixname) rref( returns the reduced row-echelon form of a real matrixname. The number of columns must be greater than or equal to the number of rows. rref(matrixname) . . . indicates that the result extends beyond the screen. To scroll the result right or left, press " or !at any time before you perform the next calculation. Matrices for the MIX 33 Page 38 rowSwap( C: Row Swap Swaps rowA and rowB of matrixname, and returns the new matrix. rowSwap(matrixname, rowA, rowB) From the original matrix, rows 2 and 4 are swapped. row+( D: Row Addition Adds rowA and rowB of matrixname, stores the sum in rowB, and returns the new matrix. row+(matrixname, rowA, rowB) From the original matrix, rows 1 and 2 are added to create this new row 2. Matrices for the MIX 33 Page 39 *row( E: Row Multiplication Multiplies a specified row of matrixname by value, stores the result in row, and returns the new matrix. ¦row(value, matrixname, row) From the original matrix, row 1 is multiplied by 2 to create this new row 1. *row+( F: Row Multiplication and Addition Multiplies rowA of matrixname by value, adds it to rowB, stores the results in rowB, and returns the new matrix. ¦row+(value, matrixname, rowA, rowB) From the original matrix, row 1 is multiplied by 3 to produce [3 6 9], which is then added to row 2. Matrices for the MIX 33 Page 40 [ , ] G: and H: Direct Matrix Entry Let you enter a matrix directly from the Matrix Home screen. [. . . ] COPYRIGHT: The Licensed Materials and any accompanying documentation are copyrighted. If you make copies, do not delete the copyright notice, trademark, or protective notices from the copies. WARRANTY: TI does not warrant that the Licensed Materials or documentation will be free from errors or that they will meet your specific requirements. THE LICENSED MATERIALS ARE PROVIDED “AS IS” TO YOU OR ANY SUBSEQUENT USER. [. . . ]