Ept 8.Let S be the port of -n 씨 back, I'm Jerry of S (a) Compute ELA (b) FindedS
-n ', S Let f(x,yZFz2_xy. Let v=<1,1,1>. Let point P=<2,1,3> a. Compute gradient of fx,y,z) b. If the contours are far apart, is the length of the gradient large or small? Answer: Explain! What MATLAB command is used to draw the gradient vectors? Answer: - c. Compute the directional derivative in the direction of v. d. Compute the equation of the tangent plane to f(x,y,z) at the point P. e. Use the chain rule to compute r if x t2,...
8. Let Maxn denote the vector space of all n x n matrices. a. Let S C Max denote the set of symmetric matrices (those satisfying AT = A). Show that S is a subspace of Mx. What is its dimension? b. Let KC Maxn denote the set of skew-symmetric matrices (those satisfying A' = -A). Show that K is a subspace of Max. What is its dimension?
MATLAB ONLY MATLAB ONLY 2. (15 pts) Let b (1) n! 20 1) (5pts) Compute b and b 2) (5pts)Let Sb and S-b find the least N in natural numer s.t k-1 S -S 0.01 3) (5pts) Plot the constant function which image is S and plot the graph of Sn where n is from 1 to N(from 2-2) 2. (15 pts) Let b (1) n! 20 1) (5pts) Compute b and b 2) (5pts)Let Sb and S-b find the...
(1 point) Let f(x) = x2 (a) Compute S.' f(x) dx. 0.25 (b) Compute the approximations L, R , Tn, and M, for n = 4, 8, and 16 for the integral in part (a). For each of these, compute the corresponding absolute error. Note: Make sure all answers are correct to six decimal places. | L4 = 0.140625 \ELI = 0.109375 R4 = TERI = 0.265625 |ET|= 0.156249 M4 = |Eml= Lg = |EL= Rg = Er = Tg...
3. (8 points) Let B-{1] [ ]} md c= {[%:) ( -;)} Both B and C are bases for R. If {x}s 1. what is {x}c? Show all of your work by hand. You may check your answer using Sage.
3. Let Y ~ N(aln, σ21n) and matrices B and A be such that BY and (n-1)s-YAY (a) Show that B = n-11, and A = 1-n-J where I is the identity matrix and J is the matrix of all ones (b) Show that A is idempotent. (c) Show that tr(A)- rank(A). ( d ) Compute AB .
please help with both a and b 16 an Let F(x, y) = (x2 - y2) it (x²+y²); let C be the path that starts at (-1,0), travels a long the xaxis to (1,0) then along the circle ² + y²= 1 counter cockwise back to (-1,0) compute the work down along the path b) Let F(x, y, z) = (x+y)i + (y-2)j + (x2-52)k Lets be the solid tetrahedron in the first octant with vertices (0,0,0), (1,0,0), (0, 1,0)...
Please provide a detailed solution. Thanks in advance. (b) Let {Xn : n E N} b e a second order Markov chain, 1.e. , for all i,j, in-1,.. . ,i1 and for all n. Transform the state space so that the resulting process s first order Markovian.
Let n > 1, and let S = {1, 2, 3}" (the cartesian product of {1,2,3} n times). (a) What is Sl? Give a brief explanation. (b) For 0 <k <n, let T be the set of all elements of S with exactly k occurrences of 3's. Determine |Tx I, and prove it using a bijection. In your solution, you need to define a set Ax that involves subsets and/or cartesian products with known cardinalities. Then clearly define your bijection...
1. (40pts) Let 8 >0 and hn: (8,2 - 8] -R be given by cos(n) hn (x) 72 Use Dirichlet's Test to show that the series hn converges uniformly on (8,27 - 8). That is, please solve the following problems: la. (10 pts) Let 9n (x) = . * € (8,27 - 8). Show that In - g uniformly, where g(x) = 0, for all 2 € (5,2 - 8) and 9n+1 () S (x). for all n e N...