-27 15 -50 28 Find an invertible 2 × 2 matrix P and a 2 × 2 diagonal matrix D such that P−¹ A6P = D. P = D = Let A =

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Q: (c) lim 2² = 2i. z→1+i

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Q: Solve the following ODES by Undetermined Coeff. X

A: Part (i): Given,                y''+5y'+4y=x2e2x

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A: Introduction: Ordinary differential equations are differential equations in which the dependent…

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A: Sol:- y''' +2y'' -9y' -18=10+20sin5tThe general solution to anxyn+...+a1xy'+a0xy=gx can be written…

Q: Define the binary operator @ by: a@b= 8b Find each of the following: d. g@k=

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Q: - y" - 5y + 4y= 2et

A: y'' -5y' +4y=2etThe general solution to axy''+bxy'+cxy=gx can be written asy=yh+ypyh is the solution…

Q: 3 Solve the following ODES by Inverse Operator method 2 • (B²+1) y = cos x Ans : y = C₁ C3 x + C₂…

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Q: Solve the following ODES by Undetermined Coeff. 1/ X 2X 2 • "Y "y + 5y + 4y = x² ²² Ans : y=c₁e +…

A: 1. To Solve: Given ODEs by Undetermined coefficients:   (a) y''+5y'+4y=x2 e2x   (b) y''-16y=19.2…

Q: 8. Consider the solutions Y(t) of Y'(t) + ay(t) = de-bt with a, b, d constants and a, b > 0.…

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Q: 33. Prove that the row vectors of an n x n invertible matrix A form a basis for Rn.

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Q: 3 dy dt³ 3 d²y dt² +2. 9 dy dt - 18 = 10 + 20sin5t

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