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Consider the two vector-functions listed below. Justify your answers for each question. x1(t) = [t, 2t]...

Consider the two vector-functions listed below. Justify your answers for each question.

x1(t) = [t, 2t] and x2(t) = [t , t^2]

(a) Are the vector-functions x1(t) and x2(t) linearly independent on the interval (−∞,∞)?
(b) Does there exist a point t0 such that the constant vectors x1(t0) and x2(t0) are linearly dependent?

(c) Can the vector-functions x1(t) and x2(t) be solutions to a first-order homogeneous linear system?

DIFF. EQUATIONS

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