Casio FX-9750G 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

92
2 (row) × 2 (column) matrix
123456
Not dimension preset
6-1 Before Performing Matrix Calculations
In the Main Menu, select the MAT icon and press wto enter the Matrix Mode and
display its initial screen.
1(DEL) ....... Delete specific matrix
2(DEL•A).... Delete all matrices
• The maximum matrix dimension (size) is 255 (rows) ×255 (columns).
kk
kk
kAbout Matrix Answer Memory (MatAns)
The calculator automatically store 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
Specify the number of rows.
cw
Specify the number of columns.
d
w
P.106

93
• 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.
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 inte-
gers up to five digits (one digit used for 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).
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).
1(DEL)
Highlighted cell (up to six digits
can be displayed)
Value in currently highlighted cell
123456
Before Performing Matrix Calculations 6 - 1

94
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(DEL•A)
2. Press 1(YES) to delete all matrices in memory or 6(NO) to abort the opera-
tion without deleting anything.
• The indicator “None” is shown for all the matrices.
123456
6 - 1 Before Performing Matrix Calculations

95
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 fand cto highlight the name of
the matrix you want to use.
2. Press w.12
MatrixA = 34
56
1(R•OP) ..... Row calculation menu
2(ROW)...... Row operation menu
3(COL) ....... 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.
1(R•OP)
1(Swap) ..... Row swap
2(xRw) ....... Scalar product for a specific row
3(xRw+) ..... Addition of scalar product of specific row to another row
4(Rw+) ....... Addition of contents of specific 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
123456
123456

96
1(R•OP)1(Swap)
Input the number of the rows you want to swap.
cw
dw
uu
uu
uTo calculate the scalar product of a row
Example To calculate the scalar product of row 2 of the following matrix 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
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
6 - 2 Matrix Cell Operations

97
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
kk
kk
kRow Operations
The following menu appears whenever you press 2(ROW) while a recalled matrix
is on the display.
2(ROW)
1(DEL) ....... Delete row
2(INS) ........ Insert row
3(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)
123456
123456
Matrix Cell Operations 6 - 2

98
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)
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)
123456
123456
6 - 2 Matrix Cell Operations

99
kk
kk
kColumn Operations
The following menu appears whenever you press 3(COL) while a recalled matrix
is on the display.
3(COL)
1(DEL) ....... Delete column
2(INS) ........ Insert column
3(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)
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
123456
123456
123456
Matrix Cell Operations 6 - 2

100
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)
123456
6 - 2 Matrix Cell Operations