# Eigenvalues, Eigenvectors, Characteristic Equation for a Matrix, Modal Matrix, Spectral Matrix and Couples System of Equations

2. The time-dependent variables z, y and z satisfy the system of equations Xdot = AX where

(a) Show that the characteristic equation for the matrix A may be written as

....

(b) In the case of A = 3 determine the corresponding eigenvector.

(c) Given that the eigenvectors corresponding to the eigenvalues .. and ... are

respectively [1 2 -2]T and [2 1 2]T.

Write down a modal matrix for A and the corresponding spectral matrix.

(d) Determine the solution to the coupled system of equations when...

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Eigenvalues, Eigenvectors, Characteristic Equation for a Matrix, Modal Matrix, Spectral Matrix and Couples System of Equations are investigated. The solution is detailed and well presented.