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Apparently FixYa rejects the link in the comments, so here is the complete post I referred to.
I am afraid you cannot use the TI8xPlus family of calculators to solve linear systems in matrix form. In this calculator, matrices must have real coefficients. You can however separate (expand) the problem into a linear system of 4 equations in 4 unknowns and try to solve it with the calculator.
define X = a+i*b Define Y=c+i*d Rewrite the first equation substituting a+i*b for X and c+i*d for y. Gather all real terms together, and all imaginary terms together on the left. You will have (8a-15b-8c) +i(15a+8b-8d) = 10 +0i This equation can be split into two equations by saying that
the real part pf the left member is equal to the real part of the right member, this gives 8a-15b-8c=10, and the imaginary part of the left member is equal to the imaginary part of the right member, this gives 15a+8b-8d=0
Similarly, you rewrite the second complex equation substituting a+ib for X and c+id for Y, then expand the binomial products, gather the real parts on the left together, and the imaginary parts on the left together. After that you equate the real part on the left to the real part on the right, and do the same for the imaginary parts.
If I did not make mistakes during the expansions and the gathering of terms you should get the following equation -(8a+8c+10d) +i*(-8b+10c-8d) =0+i*0 from which you extract an equation for the real parts, -(8a+8c+10d)=0 and another for the imaginary parts i*(-8b+10c-8d) =i*0
If I did not make mistakes (you should be able to find them, if any) your system of two linear equations with complex coefficients has been converted to a system of 4 linear equations with real coefficients.
8a-15b-8c=10 15a+8b-8d=0 8a+8c+10d=0
-8b+10c-8d =0
Now, you can in theory solve this system with help of the calculator, to find a, b, c, and d. When these are found, you can reconstruct the X and Y solutions.
Now get to work: Ascertain that my extracted equations are correct, then solve for a, b,c, and d, and reconstruct X and Y. I am no seer, but my hunch is that this system is degenerate. I will not explain what that means.
Comments:
- Sorry, I am indeed no seer and apparently the matrix is non singular. Again, if I did not make mistakes its determinant is -78884, so it can be inverted.
Apparently FixYa rejects the link in the comments, so here is the complete post I referred to.
I am afraid you cannot use the TI8xPlus family of calculators to solve
linear systems in matrix form. In this calculator, matrices must have
real coefficients. You can however separate (expand) the problem into
a linear system of 4 equations in 4 unknowns and try to solve it with
the calculator. define X = a+i*bDefine Y=c+i*dRewrite the first equation substituting a+i*b for X and
c+i*d for y.Gather all real terms together, and all imaginary terms
together on the left.You will have (8a-15b-8c) +i(15a+8b-8d) = 10 +0iThis equation can be split into two equations by saying
that
the real part pf the left member is equal to the real
part of the right member, this gives 8a-15b-8c=10, andthe imaginary part of the left member is equal to the
imaginary part of the right member, this gives 15a+8b-8d=0
Similarly,
you rewrite the second complex equation substituting a+ib for X and
c+id for Y, then expand the binomial products, gather the real parts on
the left together, and the imaginary parts on the left together. After
that you equate the real part on the left to the real part on the right,
and do the same for the imaginary parts.
If I did not make
mistakes during the expansions and the gathering of terms you should get
the following equation -(8a+8c+10d) +i*(-8b+10c-8d) =0+i*0 from
which you extract an equation for the real parts, -(8a+8c+10d)=0 and
another for the imaginary parts i*(-8b+10c-8d) =i*0
If I did not
make mistakes (you should be able to find them, if any) your system of
two linear equations with complex coefficients has been converted to a
system of 4 linear equations with real coefficients.
Now, you can in theory solve this system with
help of the calculator, to find a, b, c, and d. When these are found,
you can reconstruct the X and Y solutions.
Now get to work:
Ascertain that my extracted equations are correct, then solve for a,
b,c, and d, and reconstruct X and Y. I am no seer, but my hunch is
that this system is degenerate. I will not explain what that means.
Comments:
- Sorry, I
am indeed no seer and apparently the matrix is non singular. Again, if I
did not make mistakes its determinant is -78884, so it can be inverted.
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It sounds like the problem may be caused by trying to store a matrix to a list variable.
A relative frequency table is typically created by taking a set of data and counting the number of times each value appears in the data. This count is then divided by the total number of data points to give the relative frequency of each value.
It is likely that L1, L2, L3, and L4 are lists that contain your data, and you are trying to use them to create a relative frequency table. However, it appears that L4 may contain a matrix, which is causing an error because matrices and lists have different data types and cannot be used interchangeably.
To fix this, you will need to identify where the matrix is coming from and convert it to a list, or use a different variable that is a list. Additionally, you can check the data types of your variables by using a function like type() or class() before you create the relative frequency table.
If you are still facing issues, you can share your code and dataset or specific steps you are following to create the relative frequency table, then I can help you to identify and fix the problem.
Try entering on the same command line your calculation followed by the ToFrac command. That should work. Here is a screen capture from a TI83Plus in complex mode (a+ib).
Error Data Type mean that you entered a value or variable that is the wrong data type: • For a function (including implied multiplication) or an instruction, you entered an argument that is an invalid data type, such as a complex number where a real number is required. See Appendix A and the appropriate chapter. • In an editor, you entered a type that is not allowed, such as a matrix entered as an element in the stat list editor. See the appropriate chapter. • You attempted to store an incorrect data type, such as a matrix, to a list.
An ERR: MEMORY is given when there is not enough memory to
perform the instruction or function. To increase available memory by
deleting the contents of any variable (real or complex number, list,
matrix, Y= variable, program, Apps, AppVars, picture, graph database, or
string), follow these steps. • Press [2nd] [MEM] to display the MEMORY menu. • Press 2: Mem Mgmt/Del. • Select a variable or data that needs to be deleted and press [ENTER]. •
Use the arrow keys to move the cursor next to the item, and then press
[DEL]. The variable or data should now be deleted from the memory. When
deleting programs or Apps, a message asking for confirmation will
appear. Select 2:Yes to continue. To leave any variable screen without
deleting anything, press [2nd] [MODE].
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).
Here is some help. Please read both parts attentively.
TO COMPUTE STANDARD DEVIATION AND 2-VAR STATISTICS.
I assume
you
know the theory. I will show you the key strokes
For
1-Var statistics Press [MODE][3:STAT] [1:1-VAR].
You are ready to
enter values in the X column. Enter a number and press [=]. Cursor
jumps to second number to enter. Keep entering numbers and pressing
[=] till all numbers are in. Press the [=] key after the
last one. Press
[AC] key to clear the screen. Press
[SHIFT] [STAT] (above digit 1.) then [5:Var]. Screen displays the
statistical variables 1:n ;2: x bar; 3: x sigma n; 4:x sigma n-1. Press
the
number corresponding to the statistical value you want, ex 1:n . The
variable appears on screen. Press [=] and it will be displayed. To
display another variable press [SHIFT][STAT][5:Var][ 1,2, 3, or 4] .
To access the sum of squares sigma x^2 and the sum of data sigma x
press[SHIFT][STAT][4:SUM] then [1: for sigma x^2] or [2: for sigma x].
Press [SHIFT][STAT][6:MinMax] to access minX and maxX.
For 2-var statistics To
perform
2 variable statistics you press [MODE][3:STAT] and any of the
other regression options (except 1:1-Var). A two column template opens
where you enter the X and Y values. When finished entering data, press
[SHIFT][STAT][5:Var]. to access the different statistics. As I assumed
above, you should be able to
recognize what each variable means.
ABOUT MATRICES
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 mXnmatrix has m rows and
n columns. To perform multiplication of an kXlmatrix 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.
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).
Hello,
First stop the application that is running [2nd][Quit] or [Escape]
From Home screen
[Apps][Data/Matrix Editor/][3:new] name the data set when asked.
A table is displayed Enter the values in list c1 and c2 You can rename the variables in header.
When finished press [F5:calc]
In calculation type right arrow select 5:linReg in front of x enter c1, in front of y enter c2 and [enter] to save. the equation shows when you press [ENTER]
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