Lab 3 - way: T (p(x)) = For example, if p(x) = x 2 + 4x +...

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MATH 342-010 Differential Equations with Linear Algebra II Fall 2009 Due September 25, 2009 Homework 3 Section 6.1 (Edwards and Penney) 1. Page 381, number 5 2. Page 382, number 16 3. Page 382, number 24 4. Consider the system = X (a) Sketch the phase plane and characterize the fixed point at the origin. (b) Find the solution x(t) of this system subject to X (0) = Section 4.1 (Leon) 5. Page 182, number 3 6. Let T be a transformation from P 2 to R 2 defined in the following
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Unformatted text preview: way: T (p(x)) = For example, if p(x) = x 2 + 4x + 3, T (p(x)) = = show that T is linear and find a basis for the kernel of T. 7. Decide whether the following transformations are linear. Indicate your reasoning. (a) L : R 3 R 2 , where L(x) = (2x 3 ,x 1 + x 2 ) T . (b ) L : R 2 R 2 , where L(x) = (0, x 1 + x 2 ) T . (c) L : R 2 R, where L(x) = 4x 1 x 2 + 3. 8. Page 183, number 13 9. Page 184, number 16 10. Page 184, number 17...
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Lab 3 - way: T (p(x)) = For example, if p(x) = x 2 + 4x +...

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