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Math · Advanced Math
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71 Consider the following systern of linear equations #Alz), wher dt 0 1 01 T1 A=| 0 0 11 and Iz)=IT21, -a 1 a 23 in which a is a constant. The matrix A has eigenvectors 1/a2 corresponding respectively to the eigenvalues ri 1, r21, and r3a (a) Find a fundamental set of solutions of the system if a is not equal to 1 or-1. L (b) In the case thata : -1, lg(3) becomes the same as S(2)). Namely, there is only a single eigenvector for the repeated eigenvalues r231. Thus, one cannot use ίξ(3)erst as the third solution. Find the third linearly independent solution ir(3)) and the general solution of the system in this particular case with (c) Find a single differential equation (of third order with arbitrary constant a) that is equivalent to the system of equations given above.

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