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+--- Thread: HP-35S 3x3 matrix inversion via keyboard (/thread-2991.html)
HP-35S 3x3 matrix inversion via keyboard - Rick314 - 02-02-2015 07:29 PM
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"RE: HP-35S 3x3 matrix inversion via keyboard - Thomas Klemm - 02-03-2015 02:14 AM
(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