Chapter Matrix Calculations 26 matrix memories (Mat A through Mat Z) plus a Matrix Answer Memory (MatAns), make it possible to perform the following matrix operations.
6-1 Before Performing Matrix Calculations In the Main Menu, select the MAT icon and press w to enter the Matrix Mode and display its initial screen. 2 (row) × 2 (column) matrix 1 (DEL) ....... Delete specific matrix 2 (DEL•A) .... Delete all matrices 1 2 3 4 5 6 Not dimension preset • The maximum matrix dimension (size) is 255 (rows) × 255 (columns). k About Matrix Answer Memory (MatAns) The calculator automatically store matrix calculation results in Matrix Answer Memory.
Before Performing Matrix Calculations 6-1 • All of the cells of a new matrix contain the value 0. • If “Mem ERROR” remains next to the matrix area name after you input the dimensions, it means there is not enough free memory to create the matrix you want. u To input cell values Example To input the following data into Matrix B : 1 4 2 3 5 6 Select Mat B. c Highlighted cell (up to six digits can be displayed) w bwcwdw ewfwgw (Data is input into the highlighted cell.
6-1 Before Performing Matrix Calculations 3. Press 1 (YES) to delete the matrix or 6 (NO) to abort the operation without deleting anything. • The indicator “None” replaces the dimensions of the matrix you delete. u To delete all matrices 1. While the MATRIX list is on the display, press 2 (DEL•A). 2 (DEL•A) 1 2 3 4 5 6 2. Press 1 (YES) to delete all matrices in memory or 6 (NO) to abort the operation without deleting anything. • The indicator “None” is shown for all the matrices.
6-2 Matrix Cell Operations You can perform any of the following operations involving the cells of a matrix on the display. • Row swapping, scalar product, addition • Row deletion, insertion, addition • Column deletion, insertion, addition Use the following procedure to prepare a matrix for cell operations. 1. While the MATRIX list is on the display, use f and c to highlight the name of the matrix you want to use. 2. Press w. Matrix A = 1 2 3 4 5 6 1 (R•OP) ..... Row calculation menu 2 (ROW) ......
-2 Matrix Cell Operations 1(R•OP)1(Swap) Input the number of the rows you want to swap. cw dw u To calculate the scalar product of a row Example To calculate the scalar product of row 2 of the following matrix by 4 : Matrix A = 1 2 3 4 5 6 1(R•OP) 2(×Rw) Input multiplier value. ew Specify row number.
Matrix Cell Operations 6-2 u To add two rows together Example To add row 2 to row 3 of the following matrix : Matrix A = 1 2 3 4 5 6 1(R•OP) 4(Rw+) Specify number of row to be added. cw Specify number of row to be added to. dw k Row Operations The following menu appears whenever you press 2 (ROW) while a recalled matrix is on the display. 2 (ROW) 1 2 3 4 5 6 1 (DEL) ....... Delete row 2 (INS) ........ Insert row 3 (ADD) .......
6-2 Matrix Cell Operations u To insert a row Example To insert a new row between rows one and two of the following matrix : Matrix A = 1 2 3 4 5 6 2(ROW)c 1 2 3 4 5 6 2(INS) u To add a row Example To add a new row below row 3 of the following matrix : Matrix A = 1 2 3 4 5 6 2(ROW)cc 1 2 3 4 5 6 3(ADD) 98
Matrix Cell Operations 6-2 k Column Operations The following menu appears whenever you press 3 (COL) while a recalled matrix is on the display. 3 (COL) 1 (DEL) ....... Delete column 1 2 3 4 5 6 2 (INS) ........ Insert column 3 (ADD) .......
6-2 Matrix Cell Operations 2(INS) u To add a column Example To add a new column to the right of column 2 of the following matrix : Matrix A = 1 2 3 4 5 6 3(COL)e 1 2 3 4 5 6 3(ADD) 100
6-3 Modifying Matrices Using Matrix Commands In addition to using the MATRIX list to create and modify a matrix, you can also use matrix commands to input data and create a matrix without actually displaying it. uTo display the matrix commands 1. From the Main Menu, select the RUN icon and press w. P.31 2. Press K to display the option menu. 3. Press 2 (MAT) to display the matrix operation menu.
6-3 Modifying Matrices Using Matrix Commands Example 1 To input the following data as Matrix A : 1 3 5 2 4 6 K2(MAT) ![![b,d,f !]![c,e,g !]!]a1(Mat)aA w 1 2 3 4 5 6 Matrix name • An error (Mem ERROR) occurs if memory becomes full as you are inputting data. • You can also use the above format inside a program that inputs matrix data. u To input an identity matrix P.101 Use the matrix operation menu’s Identity command (1) to create an identity matrix.
Modifying Matrices Using Matrix Commands 6-3 w Number of rows Number of columns The display shows that Matrix A consists of two rows and three columns. k Modifying Matrices Using Matrix Commands P.101 You can also use matrix commands to assign values to and recall values from an existing matrix, to fill in all cells of an existing matrix with the same value, to combine two matrices into a single matrix, and to assign the contents of a matrix column to a list file.
6-3 Modifying Matrices Using Matrix Commands u To fill a matrix with identical values and to combine two matrices into a single matrix P.101 Use the matrix operation menu’s Fill command (3) to fill all the cells of an existing matrix with an identical value and the Augment command (5) to combine two existing matrices into a single matrix.
Modifying Matrices Using Matrix Commands Example 6-3 To assign the contents of column 2 of the following matrix to list file 1 : Matrix A = 1 2 3 4 5 6 K2(MAT) 2(M→L)1(Mat) aA,c)a Column number K1(LIST)1(List)bw 1 2 3 4 5 6 You can use Matrix Answer Memory to assign the results of the above matrix input and edit operations to a matrix variable. To do so, use the following syntax.
6-4 Matrix Calculations Use the matrix command menu to perform matrix calculation operations. u To display the matrix commands P.31 1. From the Main Menu, select the RUN icon and press w. 2. Press K to display the option menu. 3. Press 2 (MAT) to display the matrix command menu. K2(MAT) 1 2 3 4 5 6 The following describes only the matrix commands that are used for matrix arithmetic operations. 1 (Mat) ........ Mat command (matrix specification) 3 (Det) ......... Det command (determinant command) 4 (Trn) .
Matrix Calculations 6-4 Example 1 To add the following two matrices (Matrix A + Matrix B) : A= 1 1 2 1 B= 2 3 2 1 1(Mat)aA+ 1(Mat)aB 1 2 3 4 5 6 w This display indicates the following result. A+B= 3 4 4 2 Example 2 To multiply the two matrices in Example 1 (Matrix A × Matrix B) 1(Mat)aA* 1(Mat)aB 1 2 3 4 5 6 w This display indicates the following result. A×B= 4 4 6 7 • The two matrices must have the same dimensions in order to be added or subtracted.
6-4 Matrix Calculations Example 3 To multiply Matrix A (from Example 1) by a 2 × 2 identity matrix 1(Mat)aA* 6(g)1(Iden)c Number of rows and columns. 1 2 3 4 5 6 w This display indicates the following result. A×E= 1 1 2 1 k Matrix Scalar Product The following is the format for calculating a matrix scalar product, which multiplies the value in each cell of the matrix by the same value.
Matrix Calculations 6-4 k Determinant The following is the format for obtaining a determinant. Matrix Mat A 3 (Det) Example w Mat Z MatAns Obtain the determinant for the following matrix : Matrix A = 1 2 3 4 5 6 –1 –2 0 3(Det)1(Mat)aAw 1 2 3 4 5 6 This display indicates determinant |A| = –9. • Determinants can be obtained only for square matrices (same number of rows and columns). Trying to obtain a determinant for a matrix that is not square produces an error (Dim ERROR).
6-4 Matrix Calculations k Matrix Transposition A matrix is transposed when its rows become columns and its columns become rows. The following is the format for matrix transposition. Matrix Mat A 4 (Trn) Example Mat Z MatAns w To transpose the following matrix: Matrix A = 1 2 3 4 5 6 4(Trn)1(Mat)aA 1 2 3 4 5 6 w This operation produces the following result. At = 1 3 5 2 4 6 k Matrix Inversion The following is the format for matrix inversion.
Matrix Calculations Example 6-4 To invert the following matrix : Matrix A = 1 2 3 4 1(Mat)aA!X 1 2 3 4 5 6 w This operation produces the following result. –2 A–1 = 1 1.5 –0.5 • Only square matrices (same number of rows and columns) can be inverted. Trying to invert a matrix that is not square produces an error (Dim ERROR). • A matrix with a value of zero cannot be inverted. Trying to invert a matrix with value of zero produces an error (Ma ERROR).
6-4 Matrix Calculations Example To square the following matrix : Matrix A = 1 2 3 4 1(Mat)aAx 1 2 3 4 5 6 w This operation produces the following result. A2 = 7 10 15 22 k Raising a Matrix to a Power The following is the format for raising a matrix to a power. Matrix Natural number Mat A M Mat Z MatAns Example k w To raise the following matrix to the third power : Matrix A = 1 2 3 4 1(Mat)aAMd 1 2 3 4 5 6 w This operation produces the following result.
Matrix Calculations 6-4 k Determining the Absolute Value, Integer Part, Fraction Part, and Maximum Integer of a Matrix The following is the format for using a matrix in built in functions to obtain an absolute value, integer part, fraction part, and maximum integer.
