Consider the following linear differential equation x^(')(t)=Ax(t) in R^(3) with A=[[1,1,1],[2,1,-1],[0,-1,1]]. Verify that x^((1))(t)=[[0],[1],[-1]]e^(2t)" and "x^((2))(t)=[[6],[-8],[-4]]e^(-t) are solutions to the differential equation. What about lambdax^((1))(t)+mux^((2))(t) ? 4) Consider the following linear differential equation x?(t)=Ax(t) i solutionspile.com

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Consider the following linear differential equation x^(')(t)=Ax(t) in R^(3) with A=[[1,1,1],[2,1,-1],[0,-1,1]]. Verify that x^((1))(t)=[[0],[1],[-1]]e^(2t)&#34; and &#34;x^((2))(t)=[[6],[-8],[-4]]e^(-t) are solutions to the differential equation. What about lambdax^((1))(t)+mux^((2))(t) ? 4) Consider the following linear differential equation x?(t)=Ax(t) in R3 with A=???120?11?1?1?11????. Verify that x(1)(t)=???01?1????e2tandx(2)(t)=???6?8?4????e?t are solutions to the differential equation. What about ?x(1)(t)+?x(2)(t) ? solutionspile.com

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