5. Given {on (0)} 1 orthogonal in the interval (a, b). Show that ||øn + Om...
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...
show that 9- a) A is orthogonal if and only if A' is orthogonal b) A is orthogonal if and only if A is orthogonal c) A& B are orthogonal then AB is orthogonal d) A is orthogonal then det(A)=1 or det(A)=-1 9- a) A is orthogonal if and only if A' is orthogonal b) A is orthogonal if and only if A is orthogonal c) A& B are orthogonal then AB is orthogonal d) A is orthogonal then det(A)=1...
Q9: Given i = y'a, +2.raya, +3åg, and points A (2m, Om, 0), B (2m, 4m, 0), C (0,4m.0). D(0,0,0) find the circulation of H around the closed path A + B + C + D A using two different methods. (20 pts)
a) Show that the n=1 and n=2 states of the particle-in-a-box are orthogonal. b) Show that the n= 0 and n= 1 states of the harmonic oscillator are orthogonal. c) Show that the 1s and 2s states of the hydrogen atom are orthogonal.
Problem 4. a) Show that the vectors [1, −2, 1], [2, 1, 0] and [1, −2, −5] form an orthogonal basis of R 3 . b) Find the coordinates of the vector [−1, 3, 4] in that basis.
om 1. Given G(s) $2+260,8 +02 where 0 < 5 < 1, find expressions for the peak magnitude response, the frequency at which it occurs, and the 3dB bandwidth of G. Briefly describe what happens to each of these three quantities as 5 + 0 and as 5 + 1.
Show that if A and B are orthogonal matrices, then A B is an orthogonal matrix.
2. (a) Show that is an orthogonal basis for R3. (b) Find a non-zero vector v in the orthogonal complement of the space 0 Span 2,2 Do not simply compute the cross product. (c) Let A be a 5 × 2 rnatrix with linearly independent columns. Using the rank-nullity theorem applied to AT, and any other results from the course, find the dinension of Col(A) 2. (a) Show that is an orthogonal basis for R3. (b) Find a non-zero vector...
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....
Show that the wafunctions sin "/C and cos "2* are orthogonal over the interval 0sxsa. n is an integer and cOS_ are