### Table of Contents

# DM41X MATRX Simultaneous Equations

** Advantage Pac Matrix manipulaltions (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`

`A`

Option presented :

ORDER=?

`2``R/S`

Options presented:

A I DT B SE

`A`

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 |

`B`

6 R/S 2 CHS R/S

Solve the System of Equations with `SE`

`SE`

Result is now in `B`

`B`

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**

`I` `I`

Check `A`

`A`

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

Find the Determinant of `A`

`DT`

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.

— *John Pumford-Green 05/08/22 11:55*