TI-84 Plus CE:
Possible Matrix Bug?
Calculator: TI-84
Plus CE
OS Version:
5.1.5.0019 (2016)
While creating a program to determine the radius of “as-built”
circular alignments, I ran into a possible bug for the TI-84 Plus CE. The program would call for the inverse of a
matrix, and the 84 returned an error when I think it shouldn’t. This blog entry will focus on the possible
bug.
Determinant of a 3 x 3 Matrix
As we know, if the determinant of a matrix is 0, it is
singular and an inverse for the matrix cannot be calculated. For a 3 x 3 matrix
A, the determinant is calculated as:
|A| = S – U + V
Where:
S = A(1,1) * ( A(2,2) * A(3,3) – A(3,2) * A(2,3) )
U = A(1,2) * ( A(2,1) * A(3,3) – A(3,1) * A(2,3) )
V = A(1,3) * ( A(2,1) * A(3,2) – A(3,1) * A(2,2) )
Designation: A(row,
column)
The test program DET3TEST will calculate the determinant
both was: first by the det function and the long calculation.
TI-84 Plus CE Program DET3TEST
Input [D]
det([D])→T
Disp "DET FUNCTION:"
Pause T
[D](1,1)*([D](2,2)*[D](3,3)-[D](2,3)*[D](3,2))→S
[D](1,2)*([D](2,1)*[D](3,3)-[D](3,1)*[D](2,3))→U
[D](1,3)*([D](2,1)*[D](3,2)-[D](2,2)*[D](3,1))→V
Disp "LONG WAY:",S-U+V
Test Results:
As expected most calculations will generate the same
determinant using both methods.
Matrix:
4
|
6
|
3
|
0
|
1
|
-5
|
-3
|
-2
|
2
|
Determinant Function:
67
Long Way: 67
Matrix:
105
|
-262
|
360
|
435
|
415
|
360
|
676
|
330
|
360
|
Determinant Function:
-68834520
Long Way: -68834520
Matrix:
108
|
76
|
-2
|
38
|
45
|
-5
|
-2
|
-5
|
6
|
Determinant Function:
10092
Long Way: 10092
Matrix:
2100
|
7584
|
2525
|
-1666
|
1724
|
-1826
|
5200
|
8
|
7543
|
Determinant Function:
2.796336659E10
Long Way:
2.796336659E10
Matrix:
114875.56
|
4173818
|
-127000.5
|
-46154
|
82755.275
|
57400
|
27604516
|
-3.12E7
|
304898400
|
Determinant Function:
1.40693245E20
Long Way:
1.40693245E20
-123456789
|
10.54
|
48275.05
|
112466708
|
48275.05
|
-417758
|
10.554
|
-42700.889
|
37200958.69
|
Determinant Function:
-2.19786983E20
Long Way:
-2.19786983E20
-123456789
|
10.54
|
48275.05
|
112466708
|
48275.05
|
-417758
|
10.554
|
-42700.889
|
37200958.69
|
Determinant Function:
-2.19786983E20
Long Way:
-2.19786983E20
So far, so good, as we expect. Here is one matrix where it went wrong:
970057481.4792
|
776304082.7892
|
-62136.68
|
776304082.7892
|
636188513.236
|
-50267.64
|
-62136.68
|
-50267.64
|
4
|
Determinant Function: 0
Long Way:
3.043565238E12
Update (11/6/2016): I recently updated the OS for the TI-84 Plus CE to version 5.2.1.0042 (2016) and tested the determinant function on this matrix again, and still got 0.
Also, in an email from Rich Grubbs, "I have verified that the following TI calculators get the result '0' when given the same matrix: TI-nspire (3.9.0.463), TI-84 keypad in the TI-nspire (2.56MP), TI-86(1.6), TI-92+ (2.05), and TI-36X Pro (Serial K-0514B)." Thank you Rich for information! Much appreciated!
Update (11/6/2016): I recently updated the OS for the TI-84 Plus CE to version 5.2.1.0042 (2016) and tested the determinant function on this matrix again, and still got 0.
Also, in an email from Rich Grubbs, "I have verified that the following TI calculators get the result '0' when given the same matrix: TI-nspire (3.9.0.463), TI-84 keypad in the TI-nspire (2.56MP), TI-86(1.6), TI-92+ (2.05), and TI-36X Pro (Serial K-0514B)." Thank you Rich for information! Much appreciated!
I tested this matrix on Wolfram Alpha, HP Prime, and Casio
Prizm and all got the latter answer (3.043565238E12).
I have not found any other matrices with mismatching
answers.
This blog is property of Edward Shore, 2016.
