%In this activity you will find the eigenvalues and eigenvectors of a square matrix.

%Consider the following matrix.

A = [3 1 0; 0 3 1; 0 0 3]

%Use the command poly() to find the characteristic polynomial.

CharacteristicPoly = poly(A)

%Use the command roots() to find the eigenvalues.

eigenvalues = roots(CharacteristicPoly)

%The eig() command returns diagonal matrix D of eigenvalues and matrix V whose

%columns are the corresponding eigenvectors. For example, the value on the diagional

%in the first column of D is the eigenvalue associated with the eigenvector in the first

%column of V. The eigenvectors in V are normalized, each having a magnitude of 1.

[V, D] = eig(A)

Use the following matrix C for this activity. C=(6 3 -8, 0 -2 0, 1 0 -3)

%Enter the matrix C.

%Find the coefficients of the characteristic polynomial. Store them in PolyCoeffs.

%Use the command roots() to find the eigenvalues. Store them in evals.

%Use the eig() command. Store the eigenvalues in matrix eigDiag. Store the associated

%eigenvectors in eigV.