<-[[.:start]] ====== 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=? 2R/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. FIXME --- //John Pumford-Green 05/08/22 11:55// ===== Further Information ===== {{tag>}}