3) Show that the u(2,1,1) and u(2,0,0) wavefunctions are orthogonal. AY 1 (2,1, 1)= Z ge...
3. Let U E Rnxn be an orthogonal matrix, i.c., UTU = UUT-1. Show that for any vector x E Rn LXTL we have |lU 2 2. Thus the 2-norm of a vector does not change when it is multiplied by an orthogonal matrix. 3. Let U E Rnxn be an orthogonal matrix, i.c., UTU = UUT-1. Show that for any vector x E Rn LXTL we have |lU 2 2. Thus the 2-norm of a vector does not change...
7. Show that the following functions u(x, y) monic functions v(x, y) and determine f(z) = u(x,y) + iv(x, y) are harmonic, find their conjugate har- as functions of 2. 2x2 2лу — 5х — 22. Зл? — 8ху — Зу? + 2у, (а) и(х, у) (b) и(х, у) (с) и(х, у) (d) u(a, y) 2e cos y 3e" sin y, = 3e-* cos y + 5e-" sin y, = elx cos y - e y sin y, (e) u(x,...
1- 2- 3- 1 (10 points) Show that {u1, U2, U3} is an orthogonal basis for R3. Then express x as a linear 3 4 combination of the u's. u -3 U2 = 0 ,u3 5 6 -2 2 -1 (10 points) Suppose a vector y is orthogonal to vectors u and v. Prove that y is orthogonal to the vector 4u - 3v. 10. (2 points each) True or False: ( ) Eigenvalues must be nonzero scalars. ( )...
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector w = (2u - v). (b) (5] Find algebraically the vector z=3u - 2 (2) (a) [5] Write u ='(1, -5, -1) as a linear combination of v1 = (1,2,0), v2 = (0,1,-1), V3 = (2,1,1). (b) (5] Are the 4 vectors u, V1, V2, V3 linearly independent? Explain your answer. (C) (5) Are the 2 vectors V, V3 linearly independent? Explain your answer....
Exercise Set Chapter 3 Q1) Let u = (2, -2, 3), v = (1, -3, 4), and w=(3,6,-4). a) Evaluate the given expression u + v V - 3u ||u – v| u. V lju – v|w V X W ux (v x W) b) Find the angle 8 between the vector u = (2,-2,3) and v = (1, -3,4). c) Calculate the area of the parallelogram determined by the vector u and v d) Calculate the scalar triple product...
where V is an n × n orthogonal matrix and U is an m × m orthogonal matrix with entries σί, , , , , Ơr where r min{m, n), one can show that A 3 Computation of an SVD We will now compute the SVD of a simple 3 × 2 matrix. Let Answer the following questions to compute the SVD of A. 5, Determine a bases for the eigenspace of λ-11and λ-1. 6. Lastly normalize the vectors (mske...
37z-2 (a) Show using the definition of the Z-Transform that Z({3+4Uk-3} ) 2. Z 3 (b) Using operational theorems and the table of Fourier-Transforms, determine the following: i. F(6e-5te-4lt); ii. F124juw sin (11w) -7 iii. F-1 4w2- 12w + 12 (c) The Fibonacci sequence {fk), is generated via the following second order difference equation fk+2 Z-Transform technique, show that for k 2 1 fk+1 f, for k 0, with fo = 0 and fi = 1. Using the k V5...
HOMEWORK SET 3-Time Varying Fields Due date: 4/3/2019 1. A square coil, 0.60 m on a side, rotates about the x axis at ω-60π rad/s in a field B 0.80a: T, as shown in Fig 1. Find the induced voltage, 2. Given E = Em sin(cot-fba, in free space, find D, B, and H. Sketch E and H at 1-0. 3. Show that the E and H fields of Problem 2 constitute a wave traveling in the z direction. Verify...
1 point) Show that Φ(u, u) (Au + 2, u-u, 7u + u) parametrizes the plane 2x -y-z = 4, Then (a) Calculate Tu T,, and n(u, v). þ(D), where D = (u, u) : 0 < u < 9,0 < u < 3. (b) Find the area of S (c) Express f(x, y, z in terms of u and v and evaluate Is f(x, y,z) ds. (a) Tu n(u,v)- T, (b) Area(S)- (c) JIs f(z, y,2) ds- 1 point)...
2-If X1(z)Find the Z-Transform of X2[x]-X, ln +3]u[n] Find theZ-Transform of X211 ( I-hind the Inverse Z-transform of given function. a) R(Z) =- (1-e") (-(z-e-ar) 3 +282+8-1 b) F (Z) = (2-2)2(2+2) Find the Z-Transform of X2 [x] = X1 [n + 3] u [n] 3- Solve the difference equation 3 4 With initial conditions y-1] 1 and yl-2] 3 4- Let the step response of a linear, time-invariant, causal system be 72 3) ulnl 15 3 a) Find the...