Deduce that the system of difference equations

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Reference no: EM131079640

Show that the eigenvalues of the matrix

are 2, 1 and -1, and find the corresponding eigenvectors. Write down the modal matrix M and spectral matrix Λ of A, and verify that MΛ = AM.

Deduce that the system of difference equations

x(k + 1) = Ax(k)

where x(k) = [x1(k) x2(k) x3(k)]T , has a solution

x(k) = My(k)

where y(k) = Λk y(0). Find this solution, given x(0) = [1 0 0]T .

Reference no: EM131079640

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