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

Chapter

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.

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.

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.

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.

Not dimension preset

P.92

Specify the number of rows.

Specify the number of columns.

• 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.

uTo input cell values

Example To input the following data into Matrix B :

123

456

Select Mat B.

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

kDeleting Matrices

You can delete either a specific matrix or all matrices in memory.

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.

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

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.

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}

uTo swap two rows

Example To swap rows two and three of the following matrix :

Matrix A = 34

1(R·OP)1(Swap)

Input the number of the rows you want to swap.

cwdw

uTo calculate the scalar product of a row

Example To calculate the scalar product of row 2 of the following matrix,

multiplying by 4 :

Matrix A = 34

1(R·OP)2(×Rw)

Input multiplier value.

Specify row number.

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 :

Matrix A = 34

1(R·OP)3(×Rw+)

Input multiplier value.

Specify number of row whose scalar product

should be calculated.

Specify number of row where result should be

added.

uTo add two rows together

Example To add row 2 to row 3 of the following matrix :

Matrix A = 34

1(R·OP)4(Rw+)

Specify number of row to be added.

Specify number of row to be added to.

6 - 2 Matrix Cell Operations

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}

uTo delete a row

Example To delete row 2 of the following matrix :

Matrix A = 34

2(ROW)c

1(DEL)

uTo insert a row

Example To insert a new row between rows one and two of the following

matrix : 12

Matrix A = 34

2(ROW)c

2(INS)

Matrix Cell Operations 6 - 2

uTo add a row

Example To add a new row below row 3 of the following matrix :

Matrix A = 34

2(ROW)cc

3(ADD)

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}

uTo delete a column

Example To delete column 2 of the following matrix :

Matrix A = 34

3(COL)e

1(DEL)

6 - 2 Matrix Cell Operations

uTo insert a column

Example To insert a new column between columns 1 and 2 of the

following matrix :

Matrix A = 34

3(COL)e

2(INS)

uTo add a column

Example To add a new column to the right of column 2 of the following

matrix :

Matrix A = 34

3(COL)e

3(ADD)

Matrix Cell Operations 6 - 2

6-3 Modifying Matrices Using Matrix Commands

[OPTN]-[MAT]

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)}

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

P.27

P.91

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