Cofactor coefficient matrix - Texas Instruments TI-36X 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.

Here is a small sample of things you can do with matrices.

A. Define a matrix (Create it)

1. Turn calculator ON.
   
2. Press Menu,select the MAT icon and press [EXE]
3. You see a list of possible matrix labels (A, B, C,D,E,F)
4. All that have not been created have a "none" to their right
5. Highlight a matrix name and press the right arrow. Where there was "none" , you have a template 0x0.
6. That is where you specify the dimensions (mxn). example. 2x2
7. Enter the first dimension and press [EXE]
8. Enter the 2nd dimension and press [EXE]
9. A matrix template opens where you enter the coefficients left to right and up down.
10. 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..

1. These operations are accessed as follows.
2. Quit the matrix editor by pressing [Menu] and selecting the [Run] application.
   
3. Press [OPTN][F2:MAT]
4. You have the menus Mat,M(atrix)->L(ist), Det(erminant), Trn (transpose), Aug(ment) ->, Iden(tity),Dim(ension) Fill

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

1. You press the [OPTN][F2:MAT] key sequence (just above)
2. Press [F3:Det]; the command det is displayed on screen.
3. Press [F1:Mat] the identifier Mat is displayed.
4. Press [ALPHA] A; screen display det Mat A.
5. 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]



Press the F6 key to access other functions.

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.

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

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

To calculate the determinant of a matrix that is already defined.

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

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. I defined a 3x3 matrix called b
2. I defined a submatrix by removing the first row and the first column of the b matrix.
   
3. The submatrix is called min11.
   
4. Its determinant is the minor of the _11 element of matrix b.
5. 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.
6. The cofactor is represented by the last result to the right of ->cof11, that means b22*b33-b23*b32.
7. For additional information refer to your algebra book.
   

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. I defined a 3x3 matrix called b
2. I defined a submatrix by removing the first row and the first column of the b matrix.
   
3. The submatrix is called min11.
   
4. Its determinant is the minor of the _11 element of matrix b.
5. 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.
6. The cofactor is represented by the last result to the right of ->cof11, that means b22*b33-b23*b32. The cofactor is a number.
   
7. For additional information refer to your algebra book.

Note: The power of -1 that multiplies the minor of an element is
(-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.

Hi,
If you have mastered matrix manipulations on the TI calculators, it should be a breeze to learn the same on the Casios.

A. Define the matrix (Create it)

1. Turn calculator ON.
   
2. Press Menu,select the MAT icon and press [EXE]
3. You see a list of possible matrix labels (A, B, C,D,E,F)
4. All that have not been created have a "none" to their right
5. Highlight a matrix name and press the right arrow. Where there was "none" , you have a template 0x0.
6. That is where you specify the dimensions (mxn). exemple. 2x2
7. Enter the first dimension and press [EXE]
8. Enter the 2nd dimension and press [EXE]
9. A matrix template opens where you enter the coefficients left to right and up down.
10. 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

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..

1. These operations are accessed as follows.
2. Quit the matrix editor by pressing [Menu] and selecting the [Run] application.
   
3. Press [OPTN][F2:MAT]
4. 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).

1. You press the [OPTN][F2:MAT] key sequence (just above)
2. Press [F3:Det]; the command det is displayed on screen.
3. Press [F1:Mat] the identifier Mat is displayed.
4. Press [ALPHA] A; screen display det Mat A.
5. Press [EXE] to get the value of the determinant.

Square of Matrix A
[OPTN][F2:MAT] (MAT) [Alpha] A ^2 [EXE]
Product of two compatible matrices MatAXMatB
[OPTN][F2:MAT] (MAT) [Alpha] A [* ) (MAT) [ALPHA] B [EXE]

Hope it helps.
Thank you for using FixYa.

Hello,
The matrix Math tools, are accessed by pressing [2nd][MATRIX] ->>[MATH]. Scroll the list to find all row permutations, etc.
Sorry but you will have to implement your Gauss-Jordan method yourself, and interactively.
Hope it helps.

I assume you are speaking of solving a system of equations with a number of unknowns. If not, please correct me. Here's an example in practice:

If you have a system of 3 equations with 3 unknowns, you would set up your matrix so that the coefficients of each variable for a particular equation are on one row. So, given equations x + y + z = 0, 2x + 3y - 4z = 1, x + -z = -1 you would type the following into your calculator: [[1,1,1,0][2,3,-4,1][1,0,-1,-1]] and press enter to make sure you typed it correctly. notice that in the third row there is a zero, since we have zero time y for the third equation. Then row-reduce the matrix (2nd > 5 > 4 > 4 or in the CATALOG as rref). You should get out the matrix [[1,0,0,-1][0,1,0,1][0,0,1,0]]. This says that x=-1 y = 1 z=0 since my first column contained the coefficients for the x variable, the second for the y variable, and the third for the z variable. The last column contains the solution, the part on the other side of the equals sign.

Hope this helps! For more reading (from someone else; I just made this one up), check out the Wikipedia articles on Gaussian elimination and Systems of linear equations

the cofactor (C) of Matrix (A) = (det(a) times (A)^-1)t

Cof A=(detAxA^1)t

Enter a matrix for (MatA) AC
shift 4 7 gives det(_
shift 4 3 shows det(a )<-end Paren
= x shows ansx
shift 4 3 shows ansxMatA -1x
= you'll see a Matrix AC to get out
shift 4 8 gives Trn(
shift 4 6 shows Trn(MatAns) =


The Matrix graph shows all the Cofactors