HP-35S 3x3 matrix inversion via keyboard
02-02-2015, 07:29 PM
Post: #1 Rick314 Junior Member Posts: 17 Joined: Oct 2014
HP-35S 3x3 matrix inversion via keyboard
The "3*3 lin. solve" predefined equation in the HP-35S can be used to find and display the inverse of a 3x3 matrix. (I found HP-35S matrix programs online, but not this keyboard tip. Feel free to provide a link if it is already posted.) The function works by entering 12 real values to solve 3 equations in 3 unknowns for (x, y, z):

A*x + B*y + C*z = D
E*x + F*y + G*z = H
I*x + J*y + K*z = L

Using matrix notation:
Code:
 +-     -+   +- -+   +- -+ | A B C |   | x |   | D | | E F G | * | y | = | H | | I J K |   | z |   | L | +-     -+   +- -+   +- -+  +- -+   +-     -+ ^-1  +- -+  | x |   | A B C |      | D |  | y | = | E F G |    * | H |  | z |   | I J K |      | L |  +- -+   +-     -+      +- -+

By doing the "3*3 lin. solve" operation 3 times with the following D H L values, the columns of the inverse matrix can be displayed.
Code:
 +- -+   +- -+   +- -+ | 1 |   | 0 |   | 0 | | 0 |   | 1 |   | 0 | | 0 |   | 0 |   | 1 | +- -+   +- -+   +- -+

For example, to find
Code:
 +-     -+ ^-1    +-                      -+ | 8 1 9 |        | -0.762   2.238  -0.619 | | 4 2 5 |     =  | -0.619   1.381  -0.190 | | 3 6 7 |        |  0.857  -2.143   0.571 | +-     -+        +-                      -+

do the following:
Code:
 DISPLAY FIX 3 EQN Repeat ^ or v until "3*3 lin. solve" is in the bottom line. SOLVE 8  R/S  1  R/S  9  R/S  1  R/S 4  R/S  2  R/S  5  R/S  0  R/S 3  R/S  6  R/S  7  R/S  0  R/S "x = -0.762" v "y = -0.619" v "z = 0.857" EQN SOLVE R/S R/S R/S 0 R/S R/S R/S R/S 1 R/S R/S R/S R/S   R/S "x = 2.238" v "y = 1.381" v "z = -2.143" EQN SOLVE R/S R/S R/S   R/S R/S R/S R/S 0 R/S R/S R/S R/S 1 R/S "x = -0.619" v "y = -0.190" v "z = 0.571"
The same thing can be done for 2x2 matrices using the "2*2 lin. solve" predefined equation.
02-03-2015, 02:14 AM
Post: #2
 Thomas Klemm Senior Member Posts: 1,447 Joined: Dec 2013
RE: HP-35S 3x3 matrix inversion via keyboard
(02-02-2015 07:29 PM)Rick314 Wrote:  Using matrix notation:
Code:
+-     -+   +- -+   +- -+ | A B C |   | x |   | D | | E F G | * | y | = | H | | I J K |   | z |   | L | +-     -+   +- -+   +- -+

Just wanted to let you know that this forum supports LaTeX:
$\begin{bmatrix} A & B & C \\ E & F & G \\ I & J & K \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} D \\ H \\ L \end{bmatrix}$
As I'm not fluent I often use this online LaTeX equation editor.

Kind regards
Thomas
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