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  3. consider the initial value problem x?=ax, x(0)=[?4

Consider the initial value problem X?=AX, X(0)=[?4,-2], with A=[?6,0,1,?6] and X=[x(t)y(t)] (a) Find the eigenvalue ?,...

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Advance Math

Consider the initial value problem X?=AX, X(0)=[?4,-2], withA=[?6,0,1,?6] and X=[x(t)y(t)] (a) Find the eigenvalue ?, aneigenvector V1, and a generalized eigenvector V2 for thecoefficient matrix of this linear system. ?= , V1= ???? ???? , V2=???? ???? $ (b) Find the most general real-valued solution to thelinear system of differential equations. Use t as the independentvariable in your answers. X(t)=c1 ???? ???? + c2 ???? ???? (c)Solve the original initial value problem. x(t)= y(t)=

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