Wednesday, June 7, 2017

HP 20S and HP 21S: 2 x 2 Matrices Inverse and Square

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

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