"Find the complete solution to the following system of ordinary differential equations by

Eigenvalue-Eigenvector method

x1'= x2 – x3 – t

x2'= x1 + x2 – t^2

x3'= x1 + x3 - 1 + t

with the initial conditions:

(a) t = 0: x1 = 1, x2 = -1, x3 = 0.

(b) t = 0: x1 = 1, x2 = 1, x3 = 1.

Eigenvalue-Eigenvector method

x1'= x2 – x3 – t

x2'= x1 + x2 – t^2

x3'= x1 + x3 - 1 + t

with the initial conditions:

(a) t = 0: x1 = 1, x2 = -1, x3 = 0.

(b) t = 0: x1 = 1, x2 = 1, x3 = 1.

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