Diffeq Math Homework

Daniel Trinh Differential Equations Lylerly 6 March 207 PROOF If A has eigenvectors with corresponding eigenvalues are linearly independent.

I. II. III. IV. V.

Then

ASSUME the eigenvectors are linearly independent. By the definition of linear independence: ; so, if these eigenvectors were not L.E., .

VI. VII.

The eigenvalues Now it is a system of equations; multiply II by and then subtract it from IV. . Therefore, b MUST be 0. When we plug that back in, we see or,

VIII.

Thus, |a|+ |b| = 0. PROVING linear independence.