Let be an matrix and a scalar. Consider the following two systems:
Show that if is a solution of the system (l) then role="math" localid="1659701582223" is a solution of the system (ll).
Yes, is a solution of the system .
Consider and is a solution of the system and respectively.
Assume be the Eigen values of the matrix A then there exist Eigen vectors such that and where is constant.
If x(t) is the solution of the linear system localid="1659702528208" then where be the Eigen values and of matrix A.
Simplify the equation as follows.
By the definition of solution of the linear system, is a solution.
Hence, if and is a solution of the system and respectively then is a solution.
Question: Consider the interaction of two species in a habitat. We are told that the change of the populations can be moderated by the equation
where time is a measured in years.
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