Casio CFX-9970G User manual

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
6
Chapter

80
2 (row) × 2 (column) matrix
6-1 Before Performing Matrix Calculations
In the Main Menu, select the MAT icon to enter the Matrix Mode and display its
initial screen.
• {DEL}/{DEL·A} ... deletes {a specific matrix}/{all matrices}
• The maximum number of rows that can be specified for a matrix is 255, and the
maximum number of columns is 255.
kk
kk
kAbout Matrix Answer Memory (MatAns)
The calculator automatically stores matrix calculation results in MatrixAnswer
Memory. Note the following points about Matrix Answer Memory.
• Whenever you perform a matrix calculation, the current Matrix Answer Memory
contents are replaced by the new result. The previous contents are deleted and
cannot be recovered.
• Inputting values into a matrix does not affect MatrixAnswer Memory contents.
kk
kk
kCreating a Matrix
To create a matrix, you must first define its dimensions (size) in the MATRIX list.
Then you can input values into the matrix.
uu
uu
uTo specify the dimensions of a matrix
Example To create a 2-row ×3-column matrix in the area named Mat B
Highlight Mat B.
c
Not dimension preset
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81
Specify the number of rows.
cw
Specify the number of columns.
d
w
• 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.
uu
uu
uTo input cell values
Example To input the following data into Matrix B :
123
456
Select Mat B.
c
w
bwcwdw
ewfwgw
(Data is input into the highlighted cell.
Each time you press w, the highlight-
ing move to the next cell to the right.)
• Displayed cell values show positive integers up to six digits, and negative
integers up to five digits (one digit used for the negative sign). Exponential
values are shown with up to two digits for the exponent. Fractional values are
not displayed.
• You can see the entire value assigned to a cell by using the cursor keys to
move the highlighting to the cell whose value you want to view.
• The amount of memory required for a matrix is ten bytes per cell. This means
that a 3 ×3 matrix requires 90 bytes of memory (3 ×3 ×10 = 90).
Before Performing Matrix Calculations 6 - 1
Highlighted cell (up to six digits
can be displayed)
Value in currently highlighted cell

82
kk
kk
kDeleting Matrices
You can delete either a specific matrix or all matrices in memory.
uu
uu
uTo delete a specific matrix
1. While the MATRIX list is on the display, use fand cto highlight the matrix
you want to delete.
2. Press 1(DEL).
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.
uu
uu
uTo delete all matrices
1. While the MATRIX list is on the display, press 2(DEL·A).
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 - 1 Before Performing Matrix Calculations

83
6-2 Matrix Cell Operations
Use the following procedure to prepare a matrix for cell operations.
1. While the MATRIX list is on the display, use fand cto highlight the name
of the matrix you want to use.
2. Press wand the function menu with the following items appears.
• {R·OP} ... {row calculation menu}
• {ROW}/{COL} ... {row}/{column} operation menu
All of the following examples use Matrix A recalled by the above operation.
kk
kk
kRow Calculations
The following menu appears whenever you press 1(R·OP) while a recalled
matrix is on the display.
• {Swap} ... {row swap}
• {×Rw} ... {scalar product of specified row}
• {×Rw+} ... {addition of scalar product of specified row to another row}
• {Rw+} ... {addition of specified row to another row}
uu
uu
uTo swap two rows
Example To swap rows two and three of the following matrix :
12
Matrix A = 34
56
1(R·OP)1(Swap)
Input the number of the rows you want to swap.
cwdw

84
uu
uu
uTo calculate the scalar product of a row
Example To calculate the scalar product of row 2 of the following matrix,
multiplying by 4 :
12
Matrix A = 34
56
1(R·OP)2(×Rw)
Input multiplier value.
ew
Specify row number.
cw
uu
uu
uTo calculate the scalar product of a row and add the result to
another row
Example To calculate the scalar product of row 2 of the following matrix,
multiplying by 4 and add the result to row 3 :
12
Matrix A = 34
56
1(R·OP)3(×Rw+)
Input multiplier value.
ew
Specify number of row whose scalar product
should be calculated.
cw
Specify number of row where result should be
added.
dw
uu
uu
uTo add two rows together
Example To add row 2 to row 3 of the following matrix :
12
Matrix A = 34
56
1(R·OP)4(Rw+)
Specify number of row to be added.
cw
Specify number of row to be added to.
dw
6 - 2 Matrix Cell Operations

85
kk
kk
kRow Operations
The following menu appears whenever you press 2(ROW) while a recalled
matrix is on the display.
• {DEL} ... {delete row}
• {INS} ... {insert row}
• {ADD} ... {add row}
uu
uu
uTo delete a row
Example To delete row 2 of the following matrix :
12
Matrix A = 34
56
2(ROW)c
1(DEL)
uu
uu
uTo insert a row
Example To insert a new row between rows one and two of the following
matrix : 12
Matrix A = 34
56
2(ROW)c
2(INS)
Matrix Cell Operations 6 - 2

86
uu
uu
uTo add a row
Example To add a new row below row 3 of the following matrix :
12
Matrix A = 34
56
2(ROW)cc
3(ADD)
kk
kk
kColumn Operations
The following menu appears whenever you press 3(COL) while a recalled
matrix is on the display.
• {DEL} ... {delete column}
• {INS} ... {insert column}
• {ADD} ... {add column}
uu
uu
uTo delete a column
Example To delete column 2 of the following matrix :
12
Matrix A = 34
56
3(COL)e
1(DEL)
6 - 2 Matrix Cell Operations

87
uu
uu
uTo insert a column
Example To insert a new column between columns 1 and 2 of the
following matrix :
12
Matrix A = 34
56
3(COL)e
2(INS)
uu
uu
uTo add a column
Example To add a new column to the right of column 2 of the following
matrix :
12
Matrix A = 34
56
3(COL)e
3(ADD)
Matrix Cell Operations 6 - 2

88
6-3 Modifying Matrices Using Matrix Commands
[OPTN]-[MAT]
uu
uu
uTo display the matrix commands
1. From the Main Menu, select the RUN icon and press w.
2. Press Kto display the option menu.
3. Press 2(MAT) to display the matrix operation menu.
The following describes only the matrix command menu items that are used for
creating matrices and inputting matrix data.
• {Mat} ... {Mat command (matrix specification)}
• {M→L} ... {Mat→List command (assign contents of selected column to list file)}
• {Aug} ... {Augment command (link two matrices)}
• {Iden} ... {Identity command (identity matrix input)}
• {Dim} ... {Dim command (dimension check)}
• {Fill} ... {Fill command (identical cell values)}
kk
kk
kMatrix Data Input Format
The following shows the format you should use when inputting data to create a
matrix using the matrix operation menu’s Mat command.
a11 a12 a1n
a21 a22 a2n
am1am2amn
= [ [a11, a12, ..., a1n] [a21, a22, ..., a2n] .... [am1, am2, ..., amn] ]
→Mat [letter A through Z]
• The maximum value of both mand nis 255.
Example 1 To input the following data as Matrix A :
135
246
K2(MAT)
![![b,d,f
!]![c,e,g
!]!]a1(Mat)aA
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