consider the subspace W of D given by W = span(e^2x, e^-2x) show that the differential operator D maps W into itself compute f(x) = cos(x) + 2xcos(x)
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consider the subspace W of D given by W = span(e^2x, e^-2x) show that the differential operator D maps W into itself compute f(x) = cos(x) + 2xcos(x)
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- Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}Consider the subspace W of D, given by W = span(sin x, cos x). (a) Show that the differential operator D maps W into itself. (b) Find the matrix of D with respect to B = {sin x, cos x}. (c) Compute the derivative of f(x) = 3 sin x - 5 cos x indirectly and verify that it agrees with f'(x) as computed directly.Let C2(-∞,∞)={f(x) in C(-∞,∞)|f''(x) exists for all x} be the set of differential functions. Show this is a subspace of C(-∞,∞).
- Let V be the subspace of C[a, b] spanned by1, ex, e−x, and let D be the differentiation operatoron V. Find the matrix A representing D with respect to the ordered basis [1, cosh x, sinhx].Consider the subspace W of D, given by W = span(e2x, e2x cos x, e2x sin x). (a) Find the matrix of D with respect to B = {e2x, e2x cos x, e2x sin x}. (b) Compute the derivative of f(x) = 3e2x - e2xcosx+ 2e2x sin x indirectly, using and verify that it agrees with f' (x) as computed directly.Consider the subspace Wof D, given by W = span (cos x, sin x, x cos x, x sin x). (a) Find the matrix of D with respect to B = {cos x, sin x, x cos x, x sin x}. (b) Compute the derivative off(x) = cos x + 2x cos x indirectly, , and verify that it agrees withf'(x) as computed directly.
- Let W be the subspace of the space of all continuous real- valued functions spanned by {cos2 t,sin2 t, cos 2t}. Find a basis for W. What is the dimension of W?Let V be the subspace of C[a, b] spanned by1, ex, e−x, and let D be the differentiation operatoron V. Find the transition matrix S representing the change of coordinates from the ordered basis [1, ex, e−x] to the ordered basis [1, cosh x, sinhx]. [cosh x = 1 2 (ex + e−x), sinh x = 1 2 (ex − e−x).]Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of R3 spanned by x and y
- what local linearizatoin of the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1) (show all steps please)How would I find whether there is a linear algebra subspace in R^3, inclusion of zero vector, closure under vector addition or scalar multiplication?The set of all nxn matrices having trace equal to zero. is a subspace W of Mnxn(F). Find a basis for W. What is the dimension of W?