Let Vbe the vector space of functions having domain [ 0, 1T] generated by the functions

Chapter 5, Problem 15

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Let Vbe the vector space of functions having domain [ 0, 1T] generated by the functions sinx and cos x. Let D be the operation of taking the derivative with respect to x, and D 2 be the operation of taking the second derivative. Find the matrix of the linear operator D 2 + 2D + 1 of V with respect to the basis {sinx, cosx} of V. Determine the image of the element 3 sinx + cosx under this transformation.

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