How do I Calculate eigenvalues? - Office Equipment & Supplies

See image below

Set up the characteristic polynomial of degree 2. After performing some straight forward algebra you can put the polynomial in the factored form (lambda-4)^2=0
The eigenvalue lambda= 4 is of multiplicity 2. (degenerate case)

I am sorry to disappoint you but the Casio FX-986G does not handle the calculations of the eigenvalues and eigenvectors of matrices. Maybe the newer OS versions can do that.
The Graph 100+ sold in Europe (I forgot the equivalent model in North America, maybe the FX9860GII Plus) can find eigenvalues and eigenvectors. Here is how it does it. See screen capture below. Compare with your calculator to see if you have the EigVl( and EigVc( commands in the catalog.

This calculator cannot find eigenvalues and eigenvectors of matrices for you. The calculator does have many row and column operation that you can use to solve your problem. You need to know the theory of matrices, determinants, and some eigenvalue and eigenvector finding algorithms.

This calculator cannot find eigenvalues and eigenvectors of matrices for you. The calculator does have many row and column operation that you can use to solve your problem. You need to know the theory of matrices, determinants, and some eigenvalue and eigenvector finding algorithms.

You cannot calculate eigenvalues or eigenvectors with this calculator. But here is a bit of the theory of the eigenvalues .
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The FX-991ES Plus barely handles simple operations on matrices of dimensions up to 3X3. It cannot find eigenvalues or eigenvectors.

In answering your other question I did make a mistake: I looked at the wrong version of the manual. The Algebra FX 2 Plus does solve for eigenvalues. Under the CAS. Here is a screen capture to help you.

I do not own that calculator so I checked the manual. In the chapter Manual calculations it explains the use of matrices but not a single reference to eigenvalues or eigenvectors. I looked also in the advanced functions chapter but nothing on eigenvalues. I believe you will have to use the general algebraic methods for calculating eigenvalues: characteristic polynomial and its solutions. Set up the equation det (Mat A -lambda Mat I)=0 where A is your original matrix and I is the Identity matrix with same dimensions as A. The determinant will give you a polynomial equation in the eigenvalue lambda. the degree of the polynomial will be equal to the dimension of the matrix. You might want to feed the equation to the polynomial solver to find some eigenvalues.

Only FX 2 Plus can calculate Eigenvalue and Eigenvector
On main menu num 9 (CAS)
OPTN-MAT-CALC-EigVl or EigVc