HP 20S and HP 21S: 2 x 2 Matrices Inverse and Square
Let M be the 2
x 2 matrix:
M = [ [
R1, R2 ] [ R3, R4 ] ]
Store values in
R1, R2, R3, and R4 before executing the program.
HP 20S and HP 21S: Inverse of a Matrix
Output: Determinant of M in R0. If the determinant is 0, then the program terminates,
since the matrix is determined to be singular (and have normal inverse). Output:
M^-1: [ [ R5, R6 ], [ R7, R8 ] ] where
R5 = R4/det(M)
R6 = -R2/det(M)
R7 = -R3/det(M)
R8 = R4/det(M)
The keystrokes
for the HP 20S and HP 21S are the same.
|
STEP
|
CODE
|
KEY
|
|
01
|
61, 41, A
|
LBL A
|
|
02
|
22, 1
|
RCL 1
|
|
03
|
55
|
*
|
|
04
|
22, 4
|
RCL 4
|
|
05
|
65
|
-
|
|
06
|
22, 2
|
RCL 2
|
|
07
|
55
|
*
|
|
08
|
22, 3
|
RCL 3
|
|
09
|
74
|
=
|
|
10
|
21, 0
|
STO 0
|
|
11
|
26
|
R/S
|
|
12
|
61, 43
|
X=0?
|
|
13
|
61, 26
|
RTN
|
|
14
|
22, 4
|
RCL 4
|
|
15
|
41, 1
|
XEQ 1
|
|
16
|
21, 5
|
STO 5
|
|
17
|
26
|
R/S
|
|
18
|
22, 2
|
RCL 2
|
|
19
|
41, 1
|
XEQ 1
|
|
20
|
32
|
+/-
|
|
21
|
21, 6
|
STO 6
|
|
22
|
26
|
R/S
|
|
23
|
22, 3
|
RCL 3
|
|
24
|
41, 1
|
XEQ 1
|
|
25
|
32
|
+/-
|
|
26
|
21, 7
|
STO 7
|
|
27
|
26
|
R/S
|
|
28
|
22, 1
|
RCL 1
|
|
29
|
41, 1
|
XEQ 1
|
|
30
|
21, 8
|
STO 8
|
|
31
|
61, 26
|
RTN
|
|
32
|
61, 41, 1
|
LBL 1
|
|
33
|
45
|
÷
|
|
34
|
22, 0
|
RCL 0
|
|
35
|
74
|
=
|
|
36
|
61, 26
|
RTN
|
Example 1:
[ [1.9, -7],
[-3.5, 4.2] ]^-1 = [ [ -0.2542, -0.4237], [ -0.2119, -0.1150 ]]
Determinant: -16.52
Example 2:
[ [-2, 8],[5,
6] ]^-1 = [ [-0.1154, 0.1538], [ 0.0962, 0.0385] ]
Determinant: -52
HP 20S and HP 21S: Square of a Matrix
Output: [ [ M5, M6 ] [ M7, M8 ] ]
M5 = R1^2 + R2
* R3
M6 = R2 * (R1 +
R4)
M7 = R3 * (R1 +
R4)
M8 = R2 * R3 +
R4
|
STEP
|
CODE
|
KEY
|
|
01
|
61, 41, A
|
LBL A
|
|
02
|
22, 1
|
RCL 1
|
|
03
|
51, 11
|
x^2
|
|
04
|
75
|
+
|
|
05
|
22, 2
|
RCL 2
|
|
06
|
55
|
*
|
|
07
|
22, 3
|
RCL 3
|
|
08
|
74
|
=
|
|
09
|
21, 5
|
STO 5
|
|
10
|
26
|
R/S
|
|
11
|
22, 2
|
RCL 2
|
|
12
|
55
|
*
|
|
13
|
33
|
(
|
|
14
|
22, 1
|
RCL 1
|
|
15
|
75
|
+
|
|
16
|
22, 4
|
RCL 4
|
|
17
|
34
|
)
|
|
18
|
74
|
=
|
|
19
|
21, 6
|
STO 6
|
|
20
|
26
|
R/S
|
|
21
|
22, 3
|
RCL 3
|
|
22
|
55
|
*
|
|
23
|
33
|
(
|
|
24
|
22, 1
|
RCL 1
|
|
25
|
75
|
+
|
|
26
|
22, 4
|
RCL 4
|
|
27
|
34
|
)
|
|
28
|
74
|
=
|
|
29
|
21, 7
|
STO 7
|
|
30
|
26
|
R/S
|
|
31
|
22, 2
|
RCL 2
|
|
32
|
55
|
*
|
|
33
|
22, 3
|
RCL 3
|
|
34
|
75
|
+
|
|
35
|
22 ,4
|
RCL 4
|
|
36
|
51, 11
|
x^2
|
|
37
|
74
|
=
|
|
38
|
21, 8
|
STO 8
|
|
39
|
61, 26
|
RTN
|
Example 1:
[ [1.9, -7],
[-3.5, 4.2] ]^2 = [ [ 28.11, -42.7], [ -21.35, 42,14 ]]
Example 2:
[ [-2, 8],[5,
6] ]^2 = [ [ 44, 32 ], [ 20, 76 ] ]
Eddie
This blog is
property of Edward Shore, 2017