+- HP Forums (https://www.hpmuseum.org/forum)
+-- Forum: HP Software Libraries (/forum-10.html)
+--- Forum: General Software Library (/forum-13.html)
+--- Thread: (20S and 21S) Inverse and Square of a 2 x 2 Matrix (/thread-8468.html)
(20S and 21S) Inverse and Square of a 2 x 2 Matrix - Eddie W. Shore - 06-08-2017 03:49 AM
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.
Code:
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 รท
34 22, 0 RCL 0
35 74 =
36 61, 26 RTNExample 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
Code:
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 RTNExample 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 ] ]