Hello everyone, first time poster, long time reader here!(adsbygoogle = window.adsbygoogle || []).push({});

I'm an ex-math major and while I'm no longer pursuing a degree anymore in mathematics, I still continue onwards in my spare time trying to learn as much as I can about it because it's always been something I've enjoyed partaking in and sharing the knowledge with others. I did manage to pull off three years of classes at my university while as a math major. I have a pretty firm grip with calc/odes/(beginning) pdes, intro linear algebra, basic proofs and logic, intro group theory, intro complex analysis, and some very basic topology.

I decided to treat myself with an early X-Mas present of a new calculator (ti-nspire cx cas); been trying to follow along with the examples given in the manual. Anyway, I'm just puzzled about the output on my calc regarding calculating char polynomials. It currently has the operation defined as [itex]p_{A}(\lambda) = det(\lambda * I - A)[/itex] with I as the nxn ident matrix, A is any nxn square matrix. When I use the charPoly function on the calculator with the matrix [itex]A = \left(\begin{array}{ccc} 1 & 3 & 0\\ 2 & -1 & 0\\ -2 & 2 & 5 \end{array}\right)[/itex], the calc outputs [itex]-\lambda^3+5\lambda^2+7\lambda-35[/itex]

When I try to do it by hand, my answer is off by a factor of -1. Hopefully someone can point out to me where my mistake is:

So I get [itex]\lambda*I - A = \left(\begin{array}{ccc} \lambda-1 & -3 & 0\\ -2 & \lambda+1 & 0\\ 2 & -2 & \lambda-5 \end{array}\right)[/itex]

[itex]det(\lambda*I - A) = (\lambda - 1) \left|\begin{array}{cc} \lambda+1 & 0\\ -2 & \lambda-5 \end{array}\right| + 3 \left|\begin{array}{cc} -2 & 0\\ 2 & \lambda-5 \end{array}\right| [/itex]

[itex]= (\lambda-1)(\lambda+1)(\lambda-5)+3[-2(\lambda-5)][/itex]

[itex] = \lambda^3 -5\lambda^2 - 7\lambda + 35[/itex]

Not really that big of a deal per se, just trying to find where I've made a mistake; any insight would be greatly appreciated.

P.S. Hands down, PF is one of the BEST sites out there! :!!)

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# Puzzled about characteristic polynomial output from my calc

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