HP-35S 3x3 matrix inversion via keyboard

[Rick314]

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.

[Thomas Klemm]

(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