2 Determine if the statement is true or false Justify your a

2) Determine if the statement is true or false. Justify your answer with the logical argument or the counterexample. a) The origin is the only equilibrium for any linear system b) If v is the eigenvector, then any scalar multiple of v is the eigenvector.

Solution

Partially true.

The origin is the equilibrium point for any linear system since for any matrix A, A*0=0

But origin is not the only equilibrium point. If A is singular, A*c =0 for any scalar c

So in these cases, there may be more than one equilibrium point including the origin.

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b) True. If v is an eigen vector, any scalar multiple also will be an eigen vector.