determine if the set is orthogonal in the interval
determine if the set is orthogonal in the interval{sen 2nx}, n = 1,2,3... [0, 7/2).
For the set of functions {sin(x),sin(2x),sin(3x),...}=sin(nx)}, n=1,2,3,... on the interval [0,pi]. Show that the set of functions is orthogonal on [0,pi].
1. Expand the following functions in terms of the orthogonal basis {1, sin 2nr. cos 2n on the interval (0, 1): n E Z, n > 0} 2. Expand the functions in problem i în terms of the basis {sin n z n є z,n > 0} on the interval (0, 1). 1. Expand the following functions in terms of the orthogonal basis {1, sin 2nr. cos 2n on the interval (0, 1): n E Z, n > 0} 2....
(1) Let 7 =< 2,1,-2 > and 7 =< 1,2,3 >. Find two vectors and such that ✓ = 7+7, where is parallel to 7 and is orthogonal to 7.
Determine whether the set of vectors is orthonormal. If the set is only orthogonal, normalize the vectors to produce an orthonormal set. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The set of vector is orthogonal only. The normalized vectors for u, and un U1 دادن داده هادی and uz = 0 are and respectively. 1 wa (Type exact answers, using radicals as needed.) OB. The set of vectors...
Determine if the set B = {(2 3 2), (1, 1, -1)} is or is not the basis of the set generated by the set A ={(1,2,3), (5,8,7), (3,4,1)} . Note: All arrays are columns
Show that the wafunctions sin "/C and cos "2* are orthogonal over the interval 0sxsa. n is an integer and cOS_ are
Chapter 2. Legendre Polynomials Examples Show that each function set is orthogonal in the given interval with respect to the specified weight function a. {sin mx}, (-7,7], w(x) = 1 b. {1, 2, 3 (3x2 - 1)}, [-1, 1], w(x) = 1 c. {1, 1 – 2, 3 (x2 - 4x + 2)}; (0,00), w(x) = e-6 Theorem: If the set of functions {P(x)} is orthogonal, then any piece-wise contin- uous function in [a, b] can be represented by the...
(a) Check that {1, 2} is an orthogonal set with the weight function w(x) = x2 on the interval (-2,2). (b) Find a quadratic polynomial p(x) = 32 + ax + b that is orthogonal to the functions in the set, with the same weighted inner product. (c) Is this set complete, as an orthogonal set with the weighted inner product?
6. Let p;(xi = 0,... , n}, with degp;(x) = i, be a set of orthogonal polynomials with respect to the inner product f f(x)g(x) dx. Given a < b, let q(x) be the line mapping a to -1 and b to 1. Prove {p;(q(x))|i = 0,... , n} is a set of orthogonal polynomials with respect to the inner product f(x)g(x) dz, satisfying deg p;(q(x))= i - 6. Let p;(xi = 0,... , n}, with degp;(x) = i, be...
Suppose an > 0 for n = 1,2,3,... Let An = %=1 a; for n = 1,2,3,..., Suppose &j=1 a; diverges. Show that: no aj diverges. {j=11taj wat AN an+j > 1-1 i=1 AN+) AN+k a Show that &j=1 N for k = 1,2,3,..., Hence show that I diverges. Show th: .-1 for n = 1,2,3,..., Hence show that Lj=, converges. C. An