The 2 dimensional, first-order, linear-homogeneous and autonomous equa- tions, a11+a12y] a21+ a22y %3D %3D a21 a22 have derivative (Jacobian) matrix [an ay2 Explain why there exists a unique solution for any initial condition; x(to) = ro, y(to) = yo. %3D

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A: Singular Matrix

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Q: show that A is nondefective and use Theorem 7.4.3 to find eAt.

A: Given,

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Q: Consider the following system of nonhomogeneous first-order differential equations: (G :)** () ae X…

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A: Let A be a n×n square matrix and Rank (A) = 2

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Q: 1. Let Y = [Y1 Y2]T and X = [X1 X2]T be two random vectors such that Y = AX, where A is a 2 × 2…

A: Let A=a11a12a21a22, it is given that Y=Y1  Y2T=Y1Y2 and X=X1X2T=X1X2 so it follows:…