Suppose that A= | 2 0 -2 1 (1 0 0 0 -1 . Find the eigenvectors of A (a) Eigenvector with respect to the smallest eigenvalue: V1 = Preview where ői is a unit vector; (b) Eigenvector with respect to the second smallest eigenvalue: 02 = Preview where v2 is a unit vector; (c) Eigenvector with respect to the bigest eigenvalue: V3 = Preview where Uz is a unit vector. Get help: Video
2 0, find lIAlF 0 1 5. Suppose a matrix A has a SVD A-UTVT with Σ- an 2 0, find lIAlF 0 1 5. Suppose a matrix A has a SVD A-UTVT with Σ- an
2. Show that p-1 E(+1) = 2a +(*)(4+1) k=0 l=0 Hint: Fix an 0 <I<p – 1, Ask youself how many k satisfy k2 = 1 mod p.
Find the Maclaurin series of 2a. Σ Preview η =0
Suppose X ~ Íx (x10) (82+1-2)|(0 < x < 1), where 0 < θ 2, Find the UMP level α 0.02 test of Ho : θ 〉 1 versus H1 : θ 〈 1 on the basis of observing X. Determine the numerica 1 critical value for the test.
physics 2. find I1, I2, and R (not R total) 0 R 2r 2A I, Izsm 200 thov find: I ; Iz i R
To calculate 2a/2 in Excel, use the functi [Select] =NORM.DIST(alpha/2, 0, 1, TRUE) =1-NORM.DIST(alpha/2, 0, 1, TRUE) ENORM.INV(1-alpha/2, 0, 1) ENORM.INV(alpha, 0, 1) =NORM.INV(alpha/2, 0, 1) Previous
Use the inverse matrices to find (AB)-1, (AT)-1, and (2A)-1. 1 1 A-1 -[:] B-1 2 3 (a) (AB)-1 (b) (A)-1 1 (c) (2A)-1
(3) Let a > 0. In spherical coordinates, a surface is defined by r = 2a cos φ for 0 Find the volume of the solid enclosed by the surface, as a function of a. φ S (3) Let a > 0. In spherical coordinates, a surface is defined by r = 2a cos φ for 0 Find the volume of the solid enclosed by the surface, as a function of a. φ S
2a,2b, and 2c 1. Assuming x > 0, find the general solution of the following Euler equa- tions. f) 5x2y" +12xy' +2y = 0 g) 2y"xy 0 h) a2y" - 2xy =0 i) a2y"-ay-n(n + 2)y 0, where n is a positive integer a) x2y"-3ay 4y 0 b) x2y"-5ay +10y 0 c) 6x2y" +7xy - y 0 d) xy"y0 e) x2y"-3ay' +13y 0 2. Find the solution of the following problems. Before doing these prob- lems, you might want to...