(20S and 21S) Inverse and Square of a 2 x 2 Matrix

[Eddie W. Shore]

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    ÷ 
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

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    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 ] ]