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# 50g: Wrong answers finding solution to linear system and characteristic polynomial

50g Graphing Calculator

I'm having trouble doing some simple tasks on my HP 50g. First one, is solving a linear system and the second one is finding the characteristic polynomial.

I try to solve this system (the structure would be A.x = [11, -8, 0], and i'm trying to find 'x'), using NUM.SLV > Solve lin syst.

1 2 3 | 11

1 2 0 | -8

1 0 0 | 0

The result is [1.E-13, -4, 19/3]. This is clearly wrong since A. [1.E-13, -4, 19/3] isn't [11, -8, 0]. The correct answer would be [0, -4, 19/3]. I don't know if there's something wrong in the configuration or i'm making a typing mistake.

The second problem is with the matrix:

0  -1  0

7   4  2

-6  0 -2

I use Matrices > Eeigenvectors > PCAR (). The resulting polynomial is X^3 - 2X^2 - X +2. The correct answer is -X^3 + 2X^2 +X - 2, exactly the same but the signs are inverted.

I know this are easy problems and I can do them by hand but later on I have to do more complex exercises that I cannot verify manually.

I'm not an expert on the 50g, I've just started using it so I'd appreciate any help you can provide.

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## 50g: Wrong answers finding solution to linear system and characteristic polynomial

Hi,

The first problem: you are using a numerical solver. Numerical solvers have small errors, 1E-13 is a small error (within scope of a 12-digit calculating device).

You can use the symbolic LINSOLVE for exact results.

The second problem: I agree with the calculator

(I have uploaded my calculations as a picture, so may take a while to show as it waits for moderator approvement.)

-Bart
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## 50g: Wrong answers finding solution to linear system and characteristic polynomial

Hi!, @León :

Kind Regards !.
Have a nice day !.
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/
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## 50g: Wrong answers finding solution to linear system and characteristic polynomial

Bart, thank you very much! LINSOLVE gave me the exact result. About the second problem, I use the formula A - x*I, I think that's why the signs are inverted. But as the eigenvalues are correct either way, it's the same.

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