I'm trying to figure out a 3x3 magic square where the rows equal 21 18 10 and the columns equal 15 24 13 using the numbers 1-9

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

Absolutely. The square-root function is the blue g-shifted function of the y^x key, 2nd row, leftmost column.

As an example, to calculate the square root of 5, press 5 g [square-root].

Most of the squares you make will be tilted 45 degrees to the side, and their sizes will vary as well.

Start by looking for pins you can connect to create squares at a diagonal. Hint 02 You want more specifics? All right, here's the location of one of the squares. Connect the four pins in the top-left corner to form a tiny square.

Just so you know, this is the only square on the board that isn't tilted. Hint 03 The largest square contains the pin that's third from the top on the left column and the bottom pin from the far-right column.

You also need to form a small diagonal block using the two pins lined up diagonally on the bottom-left portion of the board. There are two more small squares just like this one on the board. Solution For square 1, use pins 1 and 2 from row 1, and pins 1 and 2 from row 2.

Square 2 uses pin 1 from row 4, pins 1 and 3 from row 5 and pin 1 from row 6.

Square 3 has pin 3 from row 3, pins 2 and 4 from row 4 and pin 4 from row 5.

Square 4 is formed with pin 5 from row 1, pins 4 and 6 from row 2 and pin 4 in row 3.

Square 5 involves pin 3 from row 1, pin 5 in row 2, pin 2 in row 3 and pin 3 in row 4.

Square 6 has pin 3 in row 2, pin 5 in row 3, pin 2 in row 5 and pin 3 in row 6.

Square 7 uses pin 4 in row 1, pin 1 in row 3, pin 5 from row 4 and pin 2 in row 6.

Dimensions of matrices involved in operations must match.

Here is a short summary

You can only add and subtract matrices that have the same dimensions: the numbers of rows must be equal, and the number of columns must be equal.

The multiplication of structured mathematical entities (vectors, complex numbers, matrices, etc.) is different from the multiplication of unstructured (scalar) mathematical entities (regular umbers). 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).
Let there be two matrices MatA and MatB. The dimensions are indicated as mXn where m and n are natural numbers (1,2,3...)
The product MatA(kXl) * MatB(mXn) is possible only if l=m
MatA(kX3) * MatB(3Xn) is possible and meaningful, but
MatA(kX3) * MatB(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.

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,
The maximum number of dimensions is 3. Thus the largest matrix you can create is a 3x3 matrix. To verify that, press [MODE][6:Matrix][1:MatA] to get all available dimensions (3x3 to 1x1).
Hope it helps.

You can number rows in a column by entering a number in cell A1 (usually the number 1 but youcan start with any number) and the formula (=A1+1) in the next row. The result there will be 2. Copy that formula down the rows you want to number and they will be numbered 3, 4, 5, etc. Each row adds 1 to the previous row so if you do anything that disrupts the sequence (like inserting a row between two others) you will have to copy the formulas down again to restore the sequence. You can also use the Edit-Fill-... menu command to put a series of numbers into rows. Put the starting number in th efirst row. Highlight it and the rows that you want to number and select Edit-Fill-Series... Those numbers will not change if you insert columns or move the formulas.
Or you can use the formula =ROW(A1) in any cell to return the number of that row. (The result of =ROW(A1) is the number 1 in cell A1, the result of =ROW(A2) is the number 2 in cell B2, etc. In this case inserting rows will not affect the numbering (i.e. row A5 will always be numbered 5 even if the data in it is moved down.)

From Joe-Bob's handy-dandy reference:
(wikiedia...)

Normal magic squares exist for all orders n ≥ 1 except n = 2, although the case n = 1 is trivial—it consists of a single cell containing the number 1

The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. The magic constant of a normal magic square depends only on n and has the value
For normal magic squares of order n = 3, 4, 5, …, the magic constants are:
15, 34, 65, 111, 175, 260, …

A matrix needs to be square--the number of rows must equal the number of columns.