Final answer:
The matrix exponential with eigenvalue -1 can be calculated using the formula: e^(A)t = P e^(Dt) P^(-1).
Step-by-step explanation:
The matrix exponential with eigenvalue -1 can be calculated using the formula:
e^(A)t = P e^(Dt) P^(-1)
Where A is the matrix with eigenvalues on the diagonal, P is the matrix of eigenvectors, and D is a diagonal matrix with the eigenvalues as entries.
In this case, since the eigenvalue is -1, the matrix D will be:
D = [-1 0 0]
And the resulting matrix exponential will be:
e^(A)t = P e^(Dt) P^(-1)