DM41X MATRX Simultaneous Equations

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====== DM41X : MATRX : Simultaneous Equations ======

** Advantage Pac Matrix (simple version) **

===== Background:  MATRX function =====

The Advantage Pac has quite extensive Matrix handling functions, mostly beyond anything I ever would need....

The simple ''MATRX'' program allows the entry of a square matrix (**real** or **complex**), and can calculate the ''INVERSE'' and ''DETERMINANT'' of it.

The square matrix entered can be the coefficients of a set of simultaneous equations, and entering a second matrix allows the system to be solved.

===== Use of MATRX =====

==== Simple 2x2 Matrix ====

  | 2  -3 |
  | -4  8 |


Run the ''MATRX'' program ( ''XEQ ALPHA MATRX ALPHA'')

Options presented :

  RL  CX
  
Press  ''RL'' <key>''A''</key>

Option presented : 

  ORDER=?
  
<key>''2''</key><key>''R/S''</key>

Options presented: 

  A  I  DT  B  SE

<key>''A''</key>

Enter the Matrix elements

  2 R/S
  3 CHS R/S
  4 CHS R/S
  8 R/S
  
Options presented :

  A  I  DT  B  SE
  


If ''A'' is part of a system of equations, for example

  2x - 3y = 6
  -4x + 8y = -2

Then enter matrix ''B'' 

  | 6 |
  |-2 |
  
<key>''B''</key>

  6 R/S
  2 CHS R/S


Solve the System of Equations with ''SE''

<key>''SE''</key>

Result is now in ''B''

<key>''B''</key>

  1:1 = 10.5 R/S
  2:1 = 5 R/S
  
  
This means if

  2x - 3y = 6
  -4x + 8y = -2

Then X = 10.5 and y = 5

Check

  (2 * 10.5) - (3*5) = 6
  -(4 * 10.5) + (8 * 5) = -2

CORRECT!

''A'' now holds the ''LU-Decomposition'' version of the original ''A''
To restore the contents of ''A'' to normal simply ''INVERT'' ''A'' **twice**

<key>''I''</key> <key>''I''</key>

Check ''A''

<key>''A''</key>

  1:1 = 2.00
  1:2 = -3.00
  2:1 = -4.00
  2:2 = 8.00


Find the Determinant of ''A''

<key>''DT''</key>


  DET = 4.00
  

That's pretty much all for ''MATRX'' with a **real** matrix.

=== Complex Matrix ===

You can chose ''CX'' at the beginning, and enter the **Real** and **Imaginary** parts of each Matrix element if you are dealing with a complex matrix.

<TODO>
  
--- //John Pumford-Green 05/08/22 11:55//


===== Further Information =====


{{tag>}}

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