(3) Consider f: R3- R3 defined by (u,, w)-f(r, y, :) where u=x w = 3~. Let A = {1 < x < 2, 0 < xy < 2, 0 < z < 1). Write down (i) the derivative Df as a matrix (ii) the Jacobian determinant, (ii) sketch A in (x, y. :)-space, and iv) sketch f(A) in (u. v, w)-space.
Problem 8: (11 total points) Suppose that B is a nx n matrix of the form B = Viv] + v2v + V3v3, where V1, V2, V3 € R”, n > 3 are nonzero column vector and are orthogonal. a) Show that B is a positive semidefinite matrix. b) Under which condition, B will be a positive definite matrix? c) Let A be 3x3 real symmetric matrix with eigenvalues 11 > 12 > 13. Let F be a positive definite...
(1 point) The matrix -1 -1 01 A = -16 0 Lk 0 has three distinct real eigenvalues if and only if -17.036 <k< 29.184
7. Let V = P2-{polynomials in x of degree 2 on the interval o <エく1) and let H span(1,2}, Find the vector in H (i.e., the linear function) that is closest to a2 in the sense of the distance
< 0) = 1/3, and Exercise 9.8. Suppose X has an N(u,02) distribution, P(X P(X < 1) = 2/3. What are the values of u and o?!
1. Suppose you have created a vector x in R using the command x <-c(2, 7, 3, 1, 9) . Please find the results for the following commands (2) xlc(1,3,5)] (3) x [2:4] (5) length(x) (6) x [2: length(x)1 (7) x[1: length(x)-1] (8) max(x) (9) min(x) 2. Besides the vector x in question 1, suppose you have created another vector y in R using the command y <- c(1, 2, 3, 4, 5). Please find the results for the following...
Find the Fourier series off on the given interval. <x<0 OsX< F(x) = Give the number to which the Fourier series converges at a point of discontinuity of I. (if is continuous on the given interval, enter CONTINUOUS.) Let A = PDP-1 and P and D as shown below. Compute A Let A=PDP-1 and P and D A=1901 (Simplify your answers.) Use the factorization A = PDP-1 to compute Ak, where k represents an arbitrary integer. [x-» :)+(1:10:1 2:] Diagonalize...
Suppose that f(x, y) = y V x3 + 1 on the domain D = {(x, y) | 0 < y < x < 1}. D Then the double integral of f(x, y) over D is S] f(x, y)dady - Preview Get help: Video License Points possible: 1 This is attempt 1 of 3.
Need help with this question Question 2 Find the vector v with the magnitude and direction of u = (6, -6,3) ©v=(7.-7. Ž) Ov=<7, -7,7) +=(3, -3, 7 ) ©v={}: -26) ºr=(5-7)
Suppose T: V V is a linear operator. Suppose p(x) = (1-r)(x- s) has distinct real roots (rs) and that and p(T) is the zero operator. Show that V is spanned by eigenvectors of T with eigenvalues r and s. Suppose T: V V is a linear operator. Suppose p(x) = (1-r)(x- s) has distinct real roots (rs) and that and p(T) is the zero operator. Show that V is spanned by eigenvectors of T with eigenvalues r and s.