(15C) Three Linear Equations in Three Unknowns
12-09-2018, 12:43 PM (This post was last modified: 12-09-2018 12:52 PM by Gamo.)
Post: #1
 Gamo Senior Member Posts: 565 Joined: Dec 2016
(15C) Three Linear Equations in Three Unknowns
This program solve for Simultaneous Equation in Three Unknowns.

Formula used Cramer’s Rule for a 3×3 System (with Three Variables)

Equations:

a1(X) + b1(Y) + c1(Z) = d1
a2(X) + b2(Y) + c2(Z) = d2
a3(X) + b3(Y) + c3(Z) = d3

------------------------------------
Procedure:

[E] Initialize Display 0.000000000 briefly then 0.0000

a1 [ENTER] a2 [ENTER] a3 [R/S]
b1 [ENTER] b2 [ENTER] b3 [R/S]
c1 [ENTER] c2 [ENTER] c3 [R/S]
d1 [ENTER] d2 [ENTER] d3 [R/S]

[D] Answer Determinant // If 0 "No Solution"

--------------------------------------
Example:

x - 8y + z = 4
-x + 2y + z = 2
x - y + 2z = -1

[E] 0.000000000 briefly then 0.00 // Initialize

1 [ENTER] 1 [CHS] [ENTER] 1 [R/S] display 1
8 [CHS] [ENTER] 2 [ENTER] 1 [CHS] [R/S] display -8
1 [ENTER] 1 [ENTER] 2 [R/S] display 1
4 [ENTER] 2 [ENTER] 1 [CHS] [R/S] display 4

[D] display -20.0000 // Determinant
[A] display -3.0000 // Answer X
[B] display -0.8000 // Answer Y
[C] display 0.6000 // Answer Z

------------------------------------------------------
Program:

Set Memory Reallocation as needed by this program.

13 f [DIM] [(i)]

Check to see require Memory Usage have set correctly

Press g then press and hold [MEM] display 13 14 24-4

Code:
 LBL E   // Initialize and Store Elements REG CLx FIX 9  PSE FIX 4 R/S STO 3 Rv STO 2 Rv STO 1 R/S STO 6 Rv STO 5 Rv STO 4 R/S STO 9 Rv STO 8 Rv STO 7 R/S STO .3 Rv STO .2 Rv STO .1 RTN ---------------------------- LBL D   // Determinant RCL 5 RCL 9   x RCL 8 RCL 6   x   - RCL 1   x RCL 2 RCL 9   x RCL 8 RCL 3   x   - RCL 4   x   - RCL 2 RCL 6   x RCL 5 RCL 3   x   - RCL 7   x   + STO 0   --------------------------- LBL A   // Find X RCL 5 RCL 9   x RCL 8 RCL 6   x   - RCL .1   x RCL .2 RCL 9   x RCL 8 RCL .3   x   - RCL 4   x   - RCL .2 RCL 6   x RCL 5 RCL .3   x   - RCL 7   x   + RCL 0   ÷ RTN ---------------------------- LBL B   // Find Y RCL .2 RCL 9   x RCL 8 RCL .3   x   - RCL 1   x RCL 2 RCL 9   x RCL 8 RCL 3   x   - RCL .1   x   - RCL 2 RCL .3   x RCL .2 RCL 3   x   - RCL 7   x   + RCL 0   ÷ RTN ------------------------- LBL C   // Find Z RCL 5 RCL .3   x RCL .2 RCL 6   x   - RCL 1   x RCL 2 RCL .3   x RCL .2 RCL 3   x   - RCL 4   x   - RCL 2 RCL 6    x RCL 5 RCL 3   x   - RCL .1   x   + RCL 0   ÷ RTN

Gamo
12-12-2018, 05:24 AM (This post was last modified: 08-28-2019 11:49 AM by Gamo.)
Post: #2
 Gamo Senior Member Posts: 565 Joined: Dec 2016
RE: (15C) Three Linear Equations in Three Unknowns
Using the build-in Matrix features this program help reduce the setup steps
to solve for the 3x3 Matrix of Three Equations in Three Unknown.

-------------------------------------

Procedure: ** (USER mode) **

[D] Input each elements follow by [R/S] from left to right to each three rows.
[E] Input each elements follow by [R/S] from top to bottom the last columns.

When done display show [ c 3 1 ]

--------------------------------------------------
Example: FIX 4 [USER]

x - 8y + z = 4
-x + 2y + z = 2
x - y + 2z = -1

[D] display 3.0000

1 [R/S] 8 [CHS] [R/S] 1 [R/S]
1 [CHS] [R/S] 2 [R/S] 1 [R/S]
1 [R/S] 1 [CHS] [R/S] 2 [R/S] display 2

[E] display 1.0000

4 [R/S] 2 [R/S] 1 [CHS] [R/S] display [c 3 1 ]

[R/S] display -3.0000 // X
[R/S] display -0.8000 // Y
[R/S] display 0.6000 // Z

--------------------------------------------
Program: ****[ USER mode ]****
Code:
 LBL D MATRIX 0 MATRIX 1 3 ENTER DIM A R/S LBL 1 STO A CLx R/S GTO 1 ----------------------------- LBL E 3  ENTER 1 DIM B R/S STO B R/S STO B R/S STO B RESULT C RCL MATRIX B RCL MATRIX A ÷ R/S RCL C R/S RCL C R/S RCL C RTN

Remark:

If user like to know the Determinant of this 3x3 Matrix

RCL MATRIX A
MATRIX 9

Gamo
02-02-2019, 10:39 PM
Post: #3
 Jlouis Senior Member Posts: 645 Joined: Nov 2014
RE: (15C) Three Linear Equations in Three Unknowns
Thanks, really nice
 « Next Oldest | Next Newest »

User(s) browsing this thread: 1 Guest(s)