Question: Consider the differential equation for the vector-valued function x, x^(')=Ax,A=[[-1,16],[-1,-1]] Find the eigenvalues lambda _(1),lambda _(2) and their corresponding eigenvectors v_(1),v_(2) of the coefficient matrix

Consider the differential equation for the vector-valued function x, x^(')=Ax,A=[[-1,16],[-1,-1]] Find the eigenvalues \lambda _(1),\lambda _(2) and their corresponding eigenvectors v_(1),v_(2) of the coefficient matrix A.(a) Eigenvalues: \lambda _(1),\lambda _(2)= Note: You must enter two numbers separated by a comma. (b) Eigenvector for \lambda _(1) you entered above: (c) Eigenvector for \lambda _(2) you entered above: v_(2)=(d) Use the eigenpairs you found in parts (a)-(c) to find real-valued fundamental solutions to the differential equation above. x_(1)= x_(2)= Note: To enter the vector (:u,v:) type .

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