TI84 Plus CE:
Possible Matrix Bug?
Calculator: TI84
Plus CE
OS Version:
5.1.5.0019 (2016)
While creating a program to determine the radius of “asbuilt”
circular alignments, I ran into a possible bug for the TI84 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.
TI84 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:",SU+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 TI84 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: TInspire (3.9.0.463), TI84 keypad in the TInspire (2.56MP), TI86(1.6), TI92+ (2.05), and TI36X Pro (Serial K0514B)." Thank you Rich for information! Much appreciated!
Update (11/6/2016): I recently updated the OS for the TI84 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: TInspire (3.9.0.463), TI84 keypad in the TInspire (2.56MP), TI86(1.6), TI92+ (2.05), and TI36X Pro (Serial K0514B)." 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.