question archive 1) Determine the first 4 nonzero terms of the Taylor series for the solution y φxy'' xy' x2y yy' = () of the given initial value problem, + cos()+ = 0; (0) = 1, (0) = 1
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1) Determine the first 4 nonzero terms of the Taylor series for the solution y φxy'' xy' x2y yy'
= () of the given initial value problem, + cos()+ = 0; (0) = 1, (0) = 1.
What do you expect the radius of convergence to be? Why?
2) Suppose the set of solutions for a non-homogeneous linear system is given by {c + v}, where v comes from a vector space V and c is a non-zero vector not in V. Is the set {c + v} a vector space? Explain why or why not.
3) You are given a 10 by 5 matrix A. Consider the linear function f(x) = Ax. Is it possible for f to be one-to-one? Explain why or why not.