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Casio fx-9750G Manual

6. matrix calculations
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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.
• Addition, subtraction, multiplication
• Scalar product calculations
• Determinant calculations
• Matrix transposition
• Matrix inversion
• Matrix squaring
• Raising a matrix to a specific power
• Absolute value, integer part extraction, fractional part extraction,
maximum integer calculations
• Matrix modification using matrix commands
6-1
Before Performing Matrix Calculations
6-2
Matrix Cell Operations
6-3
Modifying Matrices Using Matrix Commands
6-4
Matrix Calculations
Chapter
6

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Summary of Contents for Casio fx-9750G

  • Page 1: Matrix Calculations

    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. • Addition, subtraction, multiplication • Scalar product calculations • Determinant calculations • Matrix transposition •...

  • Page 2: Before Performing Matrix Calculations

    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 3 4 5 6 1 (DEL) ..Delete specific matrix Not dimension preset 2 (DEL•A) ..
  • Page 3 6 - 1 Before Performing Matrix Calculations • 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 dimen- sions, it means there is not enough free memory to create the matrix you want. u u u u u To input cell values Example To input the following data into Matrix B :...
  • Page 4 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 u u u u To delete all matrices 1.

  • Page 5: Matrix Cell Operations

    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.
  • Page 6 6 - 2 Matrix Cell Operations 1(R•OP)1(Swap) Input the number of the rows you want to swap. u u u u 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(R•OP) 2( Rw)
  • Page 7 6 - 2 Matrix Cell Operations u u u u u To add two rows together Example To add row 2 to row 3 of the following matrix : Matrix A = 1(R•OP) 4(Rw+) Specify number of row to be added. Specify number of row to be added to.
  • Page 8 6 - 2 Matrix Cell Operations u u u u u To insert a row Example To insert a new row between rows one and two of the following matrix : Matrix A = 2(ROW)c 3 4 5 6 2(INS) u u u u u To add a row Example To add a new row below row 3 of the following matrix :...
  • Page 9 6 - 2 Matrix Cell Operations k k k k k Column Operations The following menu appears whenever you press 3 (COL) while a recalled matrix is on the display. 3 (COL) 1 2 3 4 5 6 1 (DEL) ..Delete column 2 (INS) ..
  • Page 10 6 - 2 Matrix Cell Operations 2(INS) u u u u u To add a column Example To add a new column to the right of column 2 of the following matrix : Matrix A = 3(COL)e 4 5 6 3(ADD)

  • Page 11: Modifying Matrices Using Matrix Commands

    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. u u u u u To display the matrix commands 1.
  • Page 12 6 - 3 Modifying Matrices Using Matrix Commands Example 1 To input the following data as Matrix A : K2(MAT) ![![b,d,f !]![c,e,g !]!]a1(Mat)aA 2 3 4 5 6 Matrix name • An error (Mem ERROR) occurs if memory becomes full as you are inputting data. •...
  • Page 13 6 - 3 Modifying Matrices Using Matrix Commands Number of rows Number of columns The display shows that Matrix A consists of two rows and three columns. k k k k 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.
  • Page 14 6 - 3 Modifying Matrices Using Matrix Commands u u u u u To fill a matrix with identical values and to combine two matrices into a single matrix Use the matrix operation menu’s Fill command (3) to fill all the cells of an existing P.101 matrix with an identical value and the Augment command (5) to combine two ex- isting matrices into a single matrix.
  • Page 15 6 - 3 Modifying Matrices Using Matrix Commands Example To assign the contents of column 2 of the following matrix to list file 1 : Matrix A = K2(MAT) 2(M L)1(Mat) aA,c)a Column number K1(LIST)1(List)bw 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.

  • Page 16: Matrix Calculations

    6-4 Matrix Calculations Use the matrix command menu to perform matrix calculation operations. u u u u u To 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.
  • Page 17 6 - 4 Matrix Calculations Example 1 To add the following two matrices (Matrix A + Matrix B) : 1(Mat)aA+ 1(Mat)aB 2 3 4 5 6 This display indicates the following result. A + B = Example 2 To multiply the two matrices in Example 1 (Matrix A Matrix B) 1(Mat)aA* 1(Mat)aB...
  • Page 18 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. 2 3 4 5 6 This display indicates the following result. k k k k 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.
  • Page 19 6 - 4 Matrix Calculations k k k k k Determinant The following is the format for obtaining a determinant. Matrix Mat A 3 (Det) Mat Z MatAns Example Obtain the determinant for the following matrix : Matrix A = –1 –2 3(Det)1(Mat)aAw 2 3 4 5 6...
  • Page 20 6 - 4 Matrix Calculations k k k k 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) Mat Z MatAns Example To transpose the following matrix:...
  • Page 21 6 - 4 Matrix Calculations Example To invert the following matrix : Matrix A = 1(Mat)aA!X 2 3 4 5 6 This operation produces the following result. –2 –1 1.5 –0.5 • Only square matrices (same number of rows and columns) can be inverted. Try- ing to invert a matrix that is not square produces an error (Dim ERROR).
  • Page 22 6 - 4 Matrix Calculations Example To square the following matrix : Matrix A = 1(Mat)aAx 2 3 4 5 6 This operation produces the following result. 7 10 15 22 k k k k k Raising a Matrix to a Power The following is the format for raising a matrix to a power.
  • Page 23 6 - 4 Matrix Calculations k k k k 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 abso- lute value, integer part, fraction part, and maximum integer.

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