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Procedure to to solve 4x4 matrix

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Posted on Jan 02, 2017

SOURCE: Weather casio FX-115ES can solve 5*5 matrix

According to the manual for the Casio FX115ES, the largest matrix it solves is a 3x3.

Posted on Sep 11, 2008

SOURCE: In casio fx-991ES, i am

This post is rather exhaustive as regards the matrix capabilities of the calculator. So if the post recalls things you already know, please skip them. Matrix multiplication is at the end.

Let me explain how to create matrices. (If you know how to do it, skip
to the operations on matrices, at the end.)

First you must set
Matrix calculation

[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 matrices are available by pressing [Shift][Matrix]

[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

To add matrices MatA+MatB (MUST have identical dimensions same m and same n, m and n do not have to be the same)

To subtract MatA-MatB. (MUST have identical dimensions, see above)

To multiply MatAxMatB (See below for conditions on dimensions)

To raise a matrix to a power 2 [x2], cube [x3]

To obtain inverse of a SQUARE MatA already defined MatA[x-1]. The key [x-1] is the x to
the power -1 key. If the determinant of a matrix is zero, the matrix is singular and its inverse does not exit.

Dimensions of matrices involved in operations must match. Here is a
short summary

The multiplication of structured mathematical
entities (vectors, complex
numbers, matrices, etc.) is different from the multiplication of
unstructured (scalar) mathematical entities (regular numbers). As you
well know matrix multiplication is not commutative> This has to do
with the dimensions.

An **mXn **matrix has** m rows **and**
n columns**. To perform multiplication of an **kXl** matrix by
an **mXn** matrix you multiply each element in one row of the first
matrix by a specific element in a column of the second matrix. This
imposes a condition, namely that the number of columns of the first
matrix be equal to the number of rows of the second.

Thus, to be
able to multiply a kXl matrix by am mXn matrix, the number of columns of
the first (l) must be equal to the number of rows of the second (m).

So**
MatA(kXl) * MatB(mXn) is possible only if l=m**

MatA(kX3) *
Mat(3Xn) is possible and meaningful, but

Mat(kX3) * Mat(nX3) may not
be possible.

To get back to your calculation, make sure that the
number of columns of the first matrix is equal to the number of rows of
the second.** If this condition is not satisfied, the calculator
returns a dimension error**. The order of the matrices in the
multiplication is, shall we say, vital.

Posted on Dec 23, 2010

is the splitter rated for 3d??

Nov 17, 2013 | Startech VS440HDMI 4x4 HDMI Matrix Video...

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

There are HDBaseT HDMI Matrix solutions for applications like yours. I would recommend to visit KVMSwitchTech as they offer a wide range of 4x4 HDMI Matrix and 8x8 HDMI Matrix solutions with HDBaseT support and zone remotes.

http://www.kvmswitchtech.com/8x8-cat5e67-hdmi-matrix-switch-with-hdbaset-over-single-cat5e67-cable-includes-8-hdbaset-receivers-p50030.htm

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Apr 04, 2013 | Aten 4x4 HDMI Matrix Switch witch

What kind of problem ?

Jan 07, 2013 | 2006 Toyota Matrix 4x4

To make sure that the calculator is misbehaving, I suggest that you create a simple 4X4 matrix, that is not singular, and calculate it reduced row echelon form by hand, then use the calculator to perform the reduction. You can also generate a random 4x4 matrix and calculate the rref forms by hand and with the calculator. If the calculator is defective, try to upgrade the OS. If it is still defective, well, the deck is stacked aaginst you. It may then be time to get another one or to send it for repairs.

Jan 18, 2012 | Texas Instruments Office Equipment &...

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

I will not try to guess what you mean by "solve a matrix", but I believe that what follows will help you.

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).

If you know the theory behind systems of linear equations you can use matrices to solve the systems.

- 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).

If you know the theory behind systems of linear equations you can use matrices to solve the systems.

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

One not way would be to define a 4x4 matrix Mat A to hold the coefficients of the linear system. Then define a 4x1 column vector Mat V to hold the constants on the right.

Define a third 4x4 matrix Mat B you may leave filled with 0.

On command line, in Run Mat screen enter (Mat A) ^(-1) and store it in the zero-filled matrix Mat B. this is the inverse of Mat A.

If the inverse of Mat A exists, and it does in this case, the solution of the system is obtained as the column vector, resulting from the multiplication of Mat B by column vector Mat V

You can even shorten the procedure by just calculating ((Mat A)^-1)X (Mat V) [EXE]

To summarize

Multiplication operator is the regular [times] key.

Define a third 4x4 matrix Mat B you may leave filled with 0.

On command line, in Run Mat screen enter (Mat A) ^(-1) and store it in the zero-filled matrix Mat B. this is the inverse of Mat A.

If the inverse of Mat A exists, and it does in this case, the solution of the system is obtained as the column vector, resulting from the multiplication of Mat B by column vector Mat V

You can even shorten the procedure by just calculating ((Mat A)^-1)X (Mat V) [EXE]

To summarize

- Create 4x4 Mat A and type in the coefficients of the linear system.
- Create a 4x1 column vector Mat V for the right-hand sides
- Obtain you solution vector as ((Mat A)^-1)X (Mat V) [EXE]

- use catalog or
- in RunMat screen, press [OPTN] followed by [F2:Mat], then [F1:Mat].
- At this point the identifier is on command line, and you have to press [ALPHA] [X,Theta, T] to enter letter A.
- You use a similar key sequence to enter Mat V

Multiplication operator is the regular [times] key.

Nov 16, 2010 | Casio FX-9750GPlus Calculator

To create the matrix (in case you do not know.)

- Press [2nd][X^-1] to access the (MATRIX) menus.
- Use the right arrow key to move to the tab [EDIT]
- Under tab EDIT, press 1 to name the matrix as [A]
- A matrix template opens (default dimensions are 1x1)
- Change the dimensions to 4x4: Press digit 4 key and ENTER. Cursor move to 2nd dimension. Type in 4 and press [ENTER] to validate.
- The matrix template changes: screen shows a matrix, filled with 0.
- Enter the value of each coefficient and press [ENTER]. The cursor move to next coefficient.
- After you validate all values, press [2nd][MODE] to (QUIT) the matrix editor.

- In main calculator screen press [2nd][X^-1] to open the (MATRIX) functions.
- Use the right arrow once to highlight the [MATH] menu.
- Select [1:det(] and press [ENTER]
- The command det( echoes on main screen.
- Press [2nd][X^-1] to opent the (Matrix) menus again.
- Select the number in list that corresponds to your matrix (presumably 1:[A]) and press [ENTER]
- The command line shows det( [A]
- Complete the command by closing the parenthesis and pressing [ENTER]
- Wait for the result to be displayed.

Nov 01, 2010 | Texas Instruments TI-83 Plus Calculator

Hello,

Once matrix is defined, press [MENU][RUN]. Press [OPTN][F2:MAT][F3:Det][EXE]. Command echoes on Run screen as**det . **Press [F1:Mat] the identifier Mat echoes on screen which now displays **det Mat . **Press [ALPHA] A if the name of matrix is A. On screen **det Mat A. **Press [EXE] to get the determinant.

Hope it helps.

Once matrix is defined, press [MENU][RUN]. Press [OPTN][F2:MAT][F3:Det][EXE]. Command echoes on Run screen as

Hope it helps.

Jul 02, 2009 | Casio FX-9750GPlus Calculator

Aug 19, 2017 | Casio Office Equipment & Supplies

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