Question about Casio FX-115ES Scientific Calculator

The parameter is the name of the matrix, available from the matrix menu SHIFT 4.

Posted on Nov 09, 2010

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Posted on Jan 02, 2017

Create a square matrix at mots 3X3. Then you can multiply it by a scalar, or scare it, or calculate its determinant, and inverse. With two matrices that have the same dimensions you can perform .additions/subtractions or multiplications.

Nov 01, 2015 | Casio Office Equipment & Supplies

One example: the determinant of a 4x4 identity matrix is 1.

Use the matrix editor to create a 4x4 matrix with 1s along the main diagonal (upper-left to lower-right) and 0s elsewhere. Then use the det() function to calculate the determinant of this matrix.

Use the matrix editor to create a 4x4 matrix with 1s along the main diagonal (upper-left to lower-right) and 0s elsewhere. Then use the det() function to calculate the determinant of this matrix.

Sep 07, 2013 | Texas Instruments TI-83 Plus Calculator

You can jump to the end of the post for you answer**. **

A. Define the matrix (Create it)

Turn calculator ON.

Press Menu,select the MAT icon and press [EXE]

You see a list of possible matrix labels (A, B, C,D,E,F)

All that have not been created have a "none" to their right

Highlight a matrix name and press the right arrow. Where there was "none" , you have a template 0x0.

That is where you specify the dimensions (mxn). exemple. 2x2

Enter the first dimension and press [EXE]

Enter the 2nd dimension and press [EXE]

A matrix template opens where you enter the coefficients left to right and up down.

After each coefficient press [EXE]. Cursor moves to the next coefficient, etc.

At the bottom of the screen you have 3 menus for Row and column manipulations. But those will have to wait for now.

Press [SHIFT][QUIT] to return to the list of matrices to create new ones

**B. Operations on matrices**

Once you have one matrix, you can do operations on it: Calculate the determinant (if matrix is square), calculate its inverse, transpose, augment it, fill it, etc..

These operations are accessed as follows.

Quit the matrix editor by pressing [Menu] and selecting the [Run] application.

Press [OPTN][F2:MAT]

You have the menus Mat,M(atrix)->L(ist), Det(erminant), Trn (transpose), Aug(ment) ->, Iden(tity),Dim(ension) Fill

Exemple : calculate the determinant of a matrix A (already defined).

You press the [OPTN][F2:MAT] key sequence (just above)

Press [F3:Det]; the command det is displayed on screen.

Press [F1:Mat] the identifier Mat is displayed.

Press [ALPHA] A; screen display det Mat A.

Press [EXE] to get the value of the determinant.

**C. Square of Matrix A**

[OPTN][F2:MAT] (MAT) [Alpha] A ^2 [EXE]

**D. Product of two compatible matrices MatAXMatB**

[OPTN][F2:MAT] (MAT) [Alpha] A [*] (MAT) [ALPHA] B [EXE]

**E. Calculate the inverse of a square matrix** (Mat A)

Use commands like the ones above to display the command**Mat A**, the press the [x^-1] key. You will get the inverse if matrix can be inverted.

A. Define the matrix (Create it)

Turn calculator ON.

Press Menu,select the MAT icon and press [EXE]

You see a list of possible matrix labels (A, B, C,D,E,F)

All that have not been created have a "none" to their right

Highlight a matrix name and press the right arrow. Where there was "none" , you have a template 0x0.

That is where you specify the dimensions (mxn). exemple. 2x2

Enter the first dimension and press [EXE]

Enter the 2nd dimension and press [EXE]

A matrix template opens where you enter the coefficients left to right and up down.

After each coefficient press [EXE]. Cursor moves to the next coefficient, etc.

At the bottom of the screen you have 3 menus for Row and column manipulations. But those will have to wait for now.

Press [SHIFT][QUIT] to return to the list of matrices to create new ones

Once you have one matrix, you can do operations on it: Calculate the determinant (if matrix is square), calculate its inverse, transpose, augment it, fill it, etc..

These operations are accessed as follows.

Quit the matrix editor by pressing [Menu] and selecting the [Run] application.

Press [OPTN][F2:MAT]

You have the menus Mat,M(atrix)->L(ist), Det(erminant), Trn (transpose), Aug(ment) ->, Iden(tity),Dim(ension) Fill

Exemple : calculate the determinant of a matrix A (already defined).

You press the [OPTN][F2:MAT] key sequence (just above)

Press [F3:Det]; the command det is displayed on screen.

Press [F1:Mat] the identifier Mat is displayed.

Press [ALPHA] A; screen display det Mat A.

Press [EXE] to get the value of the determinant.

[OPTN][F2:MAT] (MAT) [Alpha] A ^2 [EXE]

[OPTN][F2:MAT] (MAT) [Alpha] A [*] (MAT) [ALPHA] B [EXE]

Use commands like the ones above to display the command

Apr 27, 2012 | Casio FX-9860G Graphic Calculator

Here is an account of what you can do with matrices on this scientific calculator. Certain precautions must be taken as concerns the dimensions of the matrices. Refer to your text book on matrix algebra.

On this calculator the largest matrices you can define have dimensions 3X3.

Once you have created a square matrix, for example matA.

You press [Shift][Matrix] [7:det] [SHIFT][MATRIX][3:MatA], close the parenthesis and press [ENTER].

If you have defined two similar matrices (same number of row and same number of columns) you can ADD them or subtract them. The operation keys are Plus and Minus as for any number.

To multiply you use the multiplication sign. The matrices must be compatible (mxn) multiplied by (nxk).

On this calculator the largest matrices you can define have dimensions 3X3.

- First you must set Matrix calculation: Press [MODE][6:Matrix].
- Then by entering one of the numbers [1:MatA] or [2:Matb] or [3:MatC] you get to choose the dimensions of the matrix (mxn].
- Once finished entering the matrix you clear the screen.
- The operations on A SINGLE matrix are available by pressing [Shift][Matrix].
- The choices are

- [1:Dim] to change the dimension of a matrix (in fact redefining the matrix)
- [2:Data] enter values in a matrix
- [3:MatA] access Matrix A
- [4:MatB] access Matrix B
- [5:MatC] access matrix C
- [6:MatAns] access the Answer Matrix (the last matrix calculated)
- [7:det] Calculate the determinant of a matrix already defined
- [8:Trn] The transpose of a matrix already defined

Once you have created a square matrix, for example matA.

You press [Shift][Matrix] [7:det] [SHIFT][MATRIX][3:MatA], close the parenthesis and press [ENTER].

If you have defined two similar matrices (same number of row and same number of columns) you can ADD them or subtract them. The operation keys are Plus and Minus as for any number.

To multiply you use the multiplication sign. The matrices must be compatible (mxn) multiplied by (nxk).

Aug 10, 2011 | Casio FX-115ES Scientific Calculator

Let your system of linear equations be [A][X]=[B] where [A] is a 3x3 matrix, [X] is column vector ( a 3x1 matrix) , and [B] is also a column vector or (3x1) matrix.

Assuming you are able to invert the [A] matrix to find [A^-1].

Multiplying on the keft by [A^-1] the system of equations you get

[A^-1].[A][X]=[A^-1][B].

But since the product [A^-1][A] is the (3x3) Identity matrix, the left side of the equation is jut [X], while the right side is [A^-1][B]. As you can see it is not [B][A^-1] .

To solve your problem, you should define your [A] matrix, define the [B] column vector (3x1) matrix, then perform the operation [A^-1][B] using the [X to -1] power key to calculate the inverse [A^-1].

Assuming you are able to invert the [A] matrix to find [A^-1].

Multiplying on the keft by [A^-1] the system of equations you get

[A^-1].[A][X]=[A^-1][B].

But since the product [A^-1][A] is the (3x3) Identity matrix, the left side of the equation is jut [X], while the right side is [A^-1][B]. As you can see it is not [B][A^-1] .

To solve your problem, you should define your [A] matrix, define the [B] column vector (3x1) matrix, then perform the operation [A^-1][B] using the [X to -1] power key to calculate the inverse [A^-1].

Jan 10, 2011 | Casio FX-115ES Scientific Calculator

When you press the OPTN key you see Tabs at the bottom of the screen. The second one from the left should be the submenu for matrix operations.. When you press F2:MAT, the new tabs are Mat, M>L (Matrix to List), Det (command to calculate the determinant etc.

Here is a detailed account of how to calculate the determinant of a square matrix.

I assume you know how to define your matrix, but I will repeat it here for others who might not know. You can skip to**Calculation**

1.Turn Calculator ON. If there are no icons, press [MENU].

Data Entry

2.Use arrows to highlight [MAT] icon. Press [ENTER]

3.Highlight the first line where it says Mat A. Use the right arrow to enter the dimensions of Matrix A. Enter 3 and press [EXE]. The cursor moves to the second dimension. Press 3 and press [ENTER].

4. The matrix entry screen appears.

5. Enter first matrix coefficient a_11 and press [ENTER]

6. Enter a_12 and [ENTER]

.....

Key in last coefficient a_33 and press [ENTER]

**Calculation**

Press [MENU] and [RUN]

Press [OPTN][F2:MAT][F3:Det] Command echoes on screen as**det**

Press [F1:Mat] echoes on screen as Mat; screen shows**det Mat**

Press [ALPHA] A The screen displays**det Mat A**

Press [ENTER] to calculate the determinant.

**If the matrix is not square, you cannot calculate its determinant.**

Here is a detailed account of how to calculate the determinant of a square matrix.

I assume you know how to define your matrix, but I will repeat it here for others who might not know. You can skip to

1.Turn Calculator ON. If there are no icons, press [MENU].

Data Entry

2.Use arrows to highlight [MAT] icon. Press [ENTER]

3.Highlight the first line where it says Mat A. Use the right arrow to enter the dimensions of Matrix A. Enter 3 and press [EXE]. The cursor moves to the second dimension. Press 3 and press [ENTER].

4. The matrix entry screen appears.

5. Enter first matrix coefficient a_11 and press [ENTER]

6. Enter a_12 and [ENTER]

.....

Key in last coefficient a_33 and press [ENTER]

Press [MENU] and [RUN]

Press [OPTN][F2:MAT][F3:Det] Command echoes on screen as

Press [F1:Mat] echoes on screen as Mat; screen shows

Press [ALPHA] A The screen displays

Press [ENTER] to calculate the determinant.

Dec 13, 2010 | Casio FX-9750GPlus Calculator

Since the largest matrix you can create on the FX-115ES is a 3X3 matrix, I am not sure it is worth it to do it on a calculator.

There is no command on the calculator that allows you to do it.

You can use the calculator to evaluate the minors for each element (the determinant of the matrix that is left when you remove the column and the row that have that element as intersection).

Here is an example how to calculate the cofactor of the _11 element of a 3X3 matrix.

(-1)^(row number + column number).

coff11=((-1)^2)*det(min11) =det(min11)

cof12=((-1)^(1+2))* det(min12)=-det(min12)

cof13=((-1)^(1+3))*det(min13)= det(min13)

cof21=((-1)^(1+2))*det(min21)= -det(min21)

etc.

There is no command on the calculator that allows you to do it.

You can use the calculator to evaluate the minors for each element (the determinant of the matrix that is left when you remove the column and the row that have that element as intersection).

Here is an example how to calculate the cofactor of the _11 element of a 3X3 matrix.

- I defined a 3x3 matrix called b
- I defined a submatrix by removing the first row and the first column of the b matrix.
- The submatrix is called min11.
- Its determinant is the minor of the _11 element of matrix b.
- The cofactor cof11 of _11 element of matrix b is the product of (-1) to the the power (1+1) and the minor of the _11 element.
- The cofactor is represented by the last result to the right of ->cof11, that means b22*b33-b23*b32. The cofactor is a number.
- For additional information refer to your algebra book.

(-1)^(row number + column number).

coff11=((-1)^2)*det(min11) =det(min11)

cof12=((-1)^(1+2))* det(min12)=-det(min12)

cof13=((-1)^(1+3))*det(min13)= det(min13)

cof21=((-1)^(1+2))*det(min21)= -det(min21)

etc.

Jan 26, 2010 | Casio FX-115ES Scientific Calculator

Hello,

I assume yoy know how to define your matrix, but I will repeat it here for others who might not know. You can skip to**Calculation**

1.Turn Calculator ON. If there are no icons, press [MENU].

Data Entry

2.Use arrows to highlight [MAT] icon. Press [ENTER]

3.Highlight the first line where it says Mat A. Use the right arrow to enter the dimensions of Matrix A. Enter 3 and press [EXE]. The cursor moves to the second dimension. Press 3 and press [ENTER].

4. The matrix entry screen appears.

5. Enter first matrix coefficient a_11 and press [ENTER]

6. Enter a_12 and [ENTER]

.....

Key in last coefficient a_33 and press [ENTER]

**Calculation**

Press [MENU] and [RUN]

Press [OPTN][F2:MAT][F3:Det] Command echoes on screen as**det**

Press [F1:Mat] echoes on screen as Mat; screen shows**det Mat**

Press [ALPHA] A The screen displays**det Mat A**

Press [ENTER] to calculate the determinant.

**If the matrix is not square, you cannot calculate its determinant.**

Hope it helps..

I assume yoy know how to define your matrix, but I will repeat it here for others who might not know. You can skip to

1.Turn Calculator ON. If there are no icons, press [MENU].

Data Entry

2.Use arrows to highlight [MAT] icon. Press [ENTER]

3.Highlight the first line where it says Mat A. Use the right arrow to enter the dimensions of Matrix A. Enter 3 and press [EXE]. The cursor moves to the second dimension. Press 3 and press [ENTER].

4. The matrix entry screen appears.

5. Enter first matrix coefficient a_11 and press [ENTER]

6. Enter a_12 and [ENTER]

.....

Key in last coefficient a_33 and press [ENTER]

Press [MENU] and [RUN]

Press [OPTN][F2:MAT][F3:Det] Command echoes on screen as

Press [F1:Mat] echoes on screen as Mat; screen shows

Press [ALPHA] A The screen displays

Press [ENTER] to calculate the determinant.

Hope it helps..

Oct 14, 2009 | Casio FX-9750GPlus Calculator

Hello,

You cannot calculate the inverse of an arbitrary matrix. It must be a square matrix (nxn) with non zero determinant. Make sure dimensions m and n are equal. (2x2), (3x3)

To calculate its determinant [Shift][MATRIX] [7:det] [SHIFT][MATRIX][3:MatA] close the right parenthesis and [=].

If determinant is different from zero then you can calculate its inverse.

If matrix MatA has already been defined, you calculate its inverse as follows;

[SHIFT][MATRIX][3:MatA] [X^-1][=]. Use the X to -1 power , the one under [MODE].

For well-behaved matrices you calculate the inverse directly without worrying about the determinant.

Hope it helps.

You cannot calculate the inverse of an arbitrary matrix. It must be a square matrix (nxn) with non zero determinant. Make sure dimensions m and n are equal. (2x2), (3x3)

To calculate its determinant [Shift][MATRIX] [7:det] [SHIFT][MATRIX][3:MatA] close the right parenthesis and [=].

If determinant is different from zero then you can calculate its inverse.

If matrix MatA has already been defined, you calculate its inverse as follows;

[SHIFT][MATRIX][3:MatA] [X^-1][=]. Use the X to -1 power , the one under [MODE].

For well-behaved matrices you calculate the inverse directly without worrying about the determinant.

Hope it helps.

Apr 16, 2009 | Casio FX-115ES Scientific Calculator

I solve your problem but there is a little mistake that I can't find but maybe you can so here what I wrote:

#include <graphics.h>

#include <stdlib.h>

#include <stdio.h>

#include <conio.h>

#include <dos.h>

#include <math.h>

#define n 3

typedef struct

{

double A[n][n];

int size;

}Matrix;

double det(Matrix mat);

Matrix cut(Matrix mat, int x);

int main(void)

{

clrscr();

double d;

Matrix mat;

mat.size=n;

mat.A[0][0]=1;

mat.A[0][1]=2;

mat.A[0][2]=3;

mat.A[1][0]=4;

mat.A[1][1]=4;

mat.A[1][2]=6;

mat.A[2][0]=7;

mat.A[2][1]=8;

mat.A[2][2]=9;

d=det(mat);

printf("%d",d);

getch();

return 0;

}

double det(Matrix mat)

{

double d=0;

if(mat.size>2)

for(int i=0;i<mat.size;i++)

d+=pow(-1,i)*mat.A[0][i]*det(cut(mat,i));

else

d=mat.A[0][0]*mat.A[1][1]-mat.A[0][1]*mat.A[1][0];

return d;

}

Matrix cut(Matrix mat, int x)

{

Matrix cutmat;

cutmat.size=mat.size-1;

for(int i=0;i<cutmat.size;i++)

for(int j=0;j<cutmat.size;j++)

if(j<x)

cutmat.A[i][j]=mat.A[i+1][j];

else

cutmat.A[i][j]=mat.A[i+1][j+1];

return cutmat;

}

Rate me if it helped!

And if you find the mistake please tell me where thanks.

#include <graphics.h>

#include <stdlib.h>

#include <stdio.h>

#include <conio.h>

#include <dos.h>

#include <math.h>

#define n 3

typedef struct

{

double A[n][n];

int size;

}Matrix;

double det(Matrix mat);

Matrix cut(Matrix mat, int x);

int main(void)

{

clrscr();

double d;

Matrix mat;

mat.size=n;

mat.A[0][0]=1;

mat.A[0][1]=2;

mat.A[0][2]=3;

mat.A[1][0]=4;

mat.A[1][1]=4;

mat.A[1][2]=6;

mat.A[2][0]=7;

mat.A[2][1]=8;

mat.A[2][2]=9;

d=det(mat);

printf("%d",d);

getch();

return 0;

}

double det(Matrix mat)

{

double d=0;

if(mat.size>2)

for(int i=0;i<mat.size;i++)

d+=pow(-1,i)*mat.A[0][i]*det(cut(mat,i));

else

d=mat.A[0][0]*mat.A[1][1]-mat.A[0][1]*mat.A[1][0];

return d;

}

Matrix cut(Matrix mat, int x)

{

Matrix cutmat;

cutmat.size=mat.size-1;

for(int i=0;i<cutmat.size;i++)

for(int j=0;j<cutmat.size;j++)

if(j<x)

cutmat.A[i][j]=mat.A[i+1][j];

else

cutmat.A[i][j]=mat.A[i+1][j+1];

return cutmat;

}

Rate me if it helped!

And if you find the mistake please tell me where thanks.

Mar 06, 2009 | Intel Computers & Internet

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