Question about Casio Algebra FX 2.0 Calculator

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Hello,

The Algebra FX 2.0 does matrix operations. The relevant chapters in the manual are Chapter 2 and Chapter 8.Here is the link.

Hope it helps.

Posted on Oct 04, 2009

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Posted on Jan 02, 2017

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This calculator can perform some operations on matrices with dimensions up to 3X3, but it cannot be used to find the rank of a matrix. Sorry.

Feb 25, 2014 | Casio FX991MS Scientific Calculator

The** row rank **of a matrix is the maximum number of linearly independent rows.

The**column rank **of a matrix is the maximum number of linearly independent columns.

However, it can be shown that for any matrix A,

row rank (A)=column rank (A).

It is called the rank of A. The rank of an mXn matrix is less than the minimum of m and n

**rank( A) less than or equal to min( m,n)**

Note. This calculator cannot determine for you the rank of a matrix. The matrix operations available on this calculator are limited, and the calculator cannot handle matrices with dimensions higher than 3X3

The

However, it can be shown that for any matrix A,

row rank (A)=column rank (A).

It is called the rank of A. The rank of an mXn matrix is less than the minimum of m and n

Note. This calculator cannot determine for you the rank of a matrix. The matrix operations available on this calculator are limited, and the calculator cannot handle matrices with dimensions higher than 3X3

Dec 15, 2013 | Casio FX570ES Scientific Calculator

This is a rather involved question and your calculator has pretty basic matrix capabilities.

The adjoint of a matrix is the transpose of the matrix of cofactors. For each element of the original matrix, you must calculate its cofactor and insert it at the same place as the element. Once you get the matrix of cofactors, you take its transpose.

As you see that will not be easy to explain without an example. Please consult a book on linear algebra. And NO, your calculator cannot perform such a feat even for a 3X3 matrix.

The adjoint of a matrix is the transpose of the matrix of cofactors. For each element of the original matrix, you must calculate its cofactor and insert it at the same place as the element. Once you get the matrix of cofactors, you take its transpose.

As you see that will not be easy to explain without an example. Please consult a book on linear algebra. And NO, your calculator cannot perform such a feat even for a 3X3 matrix.

Sep 12, 2011 | Casio FX-115ES Scientific 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

I do not own that calculator so I checked the manual. In the chapter Manual calculations it explains the use of matrices but not a single reference to eigenvalues or eigenvectors. I looked also in the advanced functions chapter but nothing on eigenvalues. I believe you will have to use the general algebraic methods for calculating eigenvalues: characteristic polynomial and its solutions. Set up the equation det (Mat A -lambda Mat I)=0 where A is your original matrix and I is the Identity matrix with same dimensions as A. The determinant will give you a polynomial equation in the eigenvalue lambda. the degree of the polynomial will be equal to the dimension of the matrix. You might want to feed the equation to the polynomial solver to find some eigenvalues.

Jun 30, 2011 | Casio Algebra FX 2.0 Calculator

The FX-991ES offers simple matrix operations like basic arithmetic, plus the slightly more complex operations determinant and inversion. Furthermore, it is limited to matrices with a maximum size of three rows and three columns.

The rank of a matrix is defined as the number of linearly independent row or column vectors. You can perform a simple partial test for square matrices by calculating the determinant of the matrix:

Unfortunately, this is all support the calculator offers. For small matrices (i.e. 4x4 or smaller), you should familiarize yourself with the Gau? Elimination Method algorithm for solving linear equation systems. It is a two-step procedure where a matrix first is converted to its row echelon form, and second to row canonical form to solve the LES.

You need to follow the algorithm only through the first part, the number of non-zero rows after this step equals the rank of the matrix. With a little exercise you will be able to do it faster on paper than trying to do it with your calculator only.

For larger matrices I suggest to use a PC with more powerful math software (Maple, Mathematica, ...) or, if you know some basic computer programming, just write the necessary program yourself, which is also a very good exercise both in programming and understanding the algorithm.

The rank of a matrix is defined as the number of linearly independent row or column vectors. You can perform a simple partial test for square matrices by calculating the determinant of the matrix:

- Enter the matrix into matrix variable MatA.
- Press [SHIFT] [4] [7] [SHIFT] [4] [3] [)] [=]

Unfortunately, this is all support the calculator offers. For small matrices (i.e. 4x4 or smaller), you should familiarize yourself with the Gau? Elimination Method algorithm for solving linear equation systems. It is a two-step procedure where a matrix first is converted to its row echelon form, and second to row canonical form to solve the LES.

You need to follow the algorithm only through the first part, the number of non-zero rows after this step equals the rank of the matrix. With a little exercise you will be able to do it faster on paper than trying to do it with your calculator only.

For larger matrices I suggest to use a PC with more powerful math software (Maple, Mathematica, ...) or, if you know some basic computer programming, just write the necessary program yourself, which is also a very good exercise both in programming and understanding the algorithm.

Jan 16, 2011 | Casio FX-115ES Scientific 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

Hi,

If I understand correctly you want to perform matrix calculations on matrices the coefficients of which may be numbers and/or letters (variables, parameters). While you can calculate on numerical matrices, you cannot do so with matrices with non numerical coefficients. this calculator does not know symbolic algebra.

For symbolic algebra and calculus you would need a calculator with a CAS, Computer Algebra System. Exemples of those are the TI89, Ti92, Ti Voyage 200 PLT, The Casio FX-Algebra, the Casio ClassPad, HP48S/X/G/GX/G+, HP49G/49G+, HP50G, HP48GII etc.

Hope it Helps.

Thanks for using FixYa and for rating this solution.

If I understand correctly you want to perform matrix calculations on matrices the coefficients of which may be numbers and/or letters (variables, parameters). While you can calculate on numerical matrices, you cannot do so with matrices with non numerical coefficients. this calculator does not know symbolic algebra.

For symbolic algebra and calculus you would need a calculator with a CAS, Computer Algebra System. Exemples of those are the TI89, Ti92, Ti Voyage 200 PLT, The Casio FX-Algebra, the Casio ClassPad, HP48S/X/G/GX/G+, HP49G/49G+, HP50G, HP48GII etc.

Hope it Helps.

Thanks for using FixYa and for rating this solution.

Dec 02, 2009 | Texas Instruments TI-83 Plus Calculator

Hello,

There is a function to calculate them for you.

In CAS, or Algebra or Tutor Modes, use the x! option

In Run-Math, press [OPTN][F6] to pan right, then [F1] to access the (PROB) menu then enter option number corresponding to x!

The way it works is as follows

number ! [EXE].

Due to memory limitations, you can calculate factorials of numbers up to 69.

Hope it helps.

There is a function to calculate them for you.

In CAS, or Algebra or Tutor Modes, use the x! option

In Run-Math, press [OPTN][F6] to pan right, then [F1] to access the (PROB) menu then enter option number corresponding to x!

The way it works is as follows

number ! [EXE].

Due to memory limitations, you can calculate factorials of numbers up to 69.

Hope it helps.

Nov 12, 2009 | Casio Algebra FX 2.0 Calculator

Hello,

**I will assume you are familiar with the basic concepts of matrix algebra**.

Turn calculator [ON]

Press [MODE][6:MATRIX]. Select the matrix you want: MatA, MatB, Matc

Let us assume you select 1: MatA.

MatA (mxn) sceen: there you specify the dimensions of the matrix, the number of rows, and the number of columns. Press 5 for a 2x2 matrix.

The matrix entry screen shows, a rectangle is highlighted. Enter there the a_11 coefficient, exemple 1.

1 [ENTER]. Highlight moves to a_12 ;

1 [ENTER] highlight moves to a_21

1 [ENTER] highlight moves to a_22

2 [ENTER] Highlight stays on a_22.

Matrix is defined. The values I used are arbitrary. Enter your own.

Suppose you want to calculate the determinant of MatA

Press [SHIFT][MATRIX][7:det][SHIFT][MATRIX][3:MatA] [)] [=]

Now you want to calculate the square of matA.

Press [SHIFT][MATRIX][3:MatA] [x^2][=]

A 2x2 matrix is displayed. It is MatA[^2].

If you define MatA, MatB, MatC y

Turn calculator [ON]

Press [MODE][6:MATRIX]. Select the matrix you want: MatA, MatB, Matc

Let us assume you select 1: MatA.

MatA (mxn) sceen: there you specify the dimensions of the matrix, the number of rows, and the number of columns. Press 5 for a 2x2 matrix.

The matrix entry screen shows, a rectangle is highlighted. Enter there the a_11 coefficient, exemple 1.

1 [ENTER]. Highlight moves to a_12 ;

1 [ENTER] highlight moves to a_21

1 [ENTER] highlight moves to a_22

2 [ENTER] Highlight stays on a_22.

Matrix is defined. The values I used are arbitrary. Enter your own.

Suppose you want to calculate the determinant of MatA

Press [SHIFT][MATRIX][7:det][SHIFT][MATRIX][3:MatA] [)] [=]

Now you want to calculate the square of matA.

Press [SHIFT][MATRIX][3:MatA] [x^2][=]

A 2x2 matrix is displayed. It is MatA[^2].

If you define MatA, MatB, MatC y

Sep 24, 2009 | Casio FX-115ES Scientific Calculator

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