Rref for 4X4 matrix does not answer correctly

An argument is of the wrong data type

What's the determinant of the numbers in matrix A? A singular matrix is a matrix whose determinant is zero.

Usually the right arrow allows you to move cursor to the right.

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:

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

The display now should show det(MatA) and the determinant of the matrix in the result. If the determinant is not 0, the rank of the matrix equals the dimension of the matrix, otherwise the rank is less than the dimension.

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.

It is just a matter of being in EXACT mode. To set your calculator in EXACT mode here's the key sequence. Press [MODE] [F3] [Up Arrow] [Up Arrow] [Right Arrow] [2] [ENTER]. Now when your in the Matrix Editor you can input your numbers in decimal form and, they will be automatically be converted to a fractional format. Pictured below is a matrix that was entered using decimal numbers and, was converted into factional form. Notice at the bottom of the screen the calculator is in EXACT mode.


Here's the same matrix in the HOME screen.



Next is the same matrix converted back to decimal numbers. Notice at the bottom of the screen the calculator is in APPROX mode.



And of course when I turn the calculator back to EXACT mode and, Re-ENTER the decimal formatted matrix in the HOME screen the fractional formatted matrix reappears.

You can use the propFrac( command but, having in the EXACT mode setting works better.

Here is copy of the answer I posted to a question on how to use Matrices. Read it carefully. It helped a few people, and there is no reason why it should not help you too. If after a bona fide effort to understand it you still have a problem, post a comment here. What I am saying, is do not just shoot the answer, try it first.

First you must set Matrix calculation
[MODE][6:Matrix].

1. 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)
2. Once finished entering the matrix you clear the screen.
   

The operations on a single matrix are available by pressing[Shift][Matrix]. They 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
  

Operations involving 2 matrices

1. To add matrices: MatA+MatB
2. To subtract: MatA-Matb
3. To multiply: MatAxMatB
4. To raise a matrix to a power 2 [x2], cube [x3]
5. To obtain inverse of MatA already defined MatA[x-1] where [x-1] is the x to the power -1 key

Dimensions of matrices involved in operations must match (see you textbook for the rules). Read the appendix to your user manual, there are several examples.

There are two options.

1) Whenever you want the answer in decimal form, place a decimal after at least one of the numbers.
For example: instead of using (1/2) use (1/2.)

2) Press the "Mode" button. Scroll down the list that appears until you find "Exact/Approx". If you set it to "Approximate", then it will always give the answer in decimal form. If you set it to "Exact", it will give the answer in fraction form.

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

i tried to graph a simple function but it wont show the lines it will only show the graph

Go to your matrix button and enter a "3x4" matrix.

Then enter it as follows:

-3 4 5 7
4 3 2 9
-5 5 3 -10

Then exit out and go to "2nd->matrix->math->rref(". Then press enter.

Your screen should look like this:

rref(

Then go to matrix and select your 3x4 matrix, press enter and close it with a parathesis. Your screen should look like this:

rref([A])

Press enter and the screen should say this:

1 0 0 2
0 1 0 -3
0 0 1 5

So,
x=3
y=-3
z=5

Hope this cleared up the confusion!

SJ_Sharks