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# If A = 14 1 32 1 3 4 1 , determine all values of the constant k for which the linear ISBN: 9780321964670 380

## Solution for problem 64 Chapter 3.2

Differential Equations | 4th Edition

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Problem 64

If A = 14 1 32 1 3 4 1 , determine all values of the constant k for which the linear system (Ak I3)x = 0 has an infinite number of solutions, and find the corresponding solutions.

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Product Rule If F(x)=f(x)g(x), Then F’(x)=f(x)g’(x) + f’(x)g(x) Ex. d/dx [ (4x^3 - x^2 -1)(x^3 -2x^2 + 3x +1)] = (4x^3 - X^2 - 1) (3x^2- 4x + 3) = (12x^2 -2x)(x^3 - 2x^2 + 3x + 1) However the product rule is more useful for the product of different types of functions Ex. f(x)= x^2cos(x) g(x) = e^x arctan(x) Proof of the Product Rule Let F(x) = f(x)g(x) F’(x) =...

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##### ISBN: 9780321964670

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