Show that (3.41) makes (3.42) and
Show that (3.42) makes (3.43)
Show that (3.41) makes (3.42) and Show that (3.42) makes (3.43) ol L AK ち chrth...
5. Consider the language L = {1'0/1k e {0,1}* |i >01) >0 Ak = i*j}; to show that Lis! not a regular language using pumping lemma, the correct choice for the word is: a. 10011 x=1- b. 1POP 1P Z=1 Le 1290? 12p* Z=1P OPS 2P Y-101 YEK d. 10P1P y=1" t:P
(d) Show that if L E Mn is upper triangular, th LL, and argue that IAgIP-lAollF, where IIA]IF、/tr(ATA) represents the Frobenius norm of A, and tr(A)-Σ.1 A" is the trace of A. (e) Assu me that an upper triangular matrix L has the block structure し11 し12 0 In with the size of the Ln blook being m × m. Let A-LTL, and λ = LLT. Show that tr(A (1 : m, 1 : m))-tr(A(1 : m, 1 : m))...
3. Let B ERnxn be a symmetrie and P.D. matrix. Show that l s (o Bu) (B-v) for any nonzero v E R", and that the equality holds if and only if v is an eigenvector of B. (Hnt: note that llt -W/2t, B-1/2v), and use the Cauchy-Schwarz inequality.) 4. Let (ak) be a real sequence such that for each k, either akil > ak or akt? where, is a constant independent of k. Show that a 2 min(ai, T)...
Let p E [0,1] with pメ, and let (Xn)n=o b l e the Markov chain on with initia [0,1] given by distribution δο and transition matrix 11: Z Z ify=x-1 p 0 otherwise. Use the strong law of large numbers to show that each state is transient. Hint: consider another Markov chain with additional structure but with the same distribution and transition matrix Let p E [0,1] with pメ, and let (Xn)n=o b l e the Markov chain on with...
using the attached image answer the 2 questions show all work and all conversion factors. l. A 3.41 g sample of a metallic element, M, reacts completely with 0,0158 moles of a gas, X2. to form 4.52 g of MX, What are the identities of M and X? 2. A mixture of Fezoy and Feo was found to contain 72.00% Fe by mass. What is the mass of Felo in 0.500 g of this mixture?
l. Assume that j : R-→ R-s C and satisfies what are known as the Cauchy-Riemann equations: (c) Let r-(r1, 2) and (s1, s2) be vectors in IR2 and suppose that (ri, 2)f(s1, 82) and Df(81,82)メ0. Show that f-1 satisfies the Cauchy-Riemann equations when evaluated at r. (Hint: Might I make a notational suggestion: Leta(s) = sim) = % (n, s) and b(s) 쓺(81, 82) =-警( )) 81,82 (d) For this last bit, drop the assumption that f satisfies the...
this is from measurement and instruction. looking for solution to understand better . 3.43. in a particular measurement system, quantity x is caicuiated by subtracting a measurement of a quantity : from a measurement of a quantity y, that is, xy- if the possible measurement errors in y and: are tay and b, respectively, show that the value of x can be expressed as-y(ay -bz). (a) What is inconvenient about this expression for x, and what is the basis for...
1. Show that the Lagrangians L(t,q, y) and Īct, 4, ) = L(1,4,0) + f/10, 9) yield the same Euler-Lagrange equations. Here q e R and f(t,q) is an arbitrary function. 2 Lagrangian mechanics In mechanics, the space where the motion of a system lies is called the configuration space, which is usually an n-dimensional manifold Q. Motion of a system is defined as a curve q : R + Qon Q. Conventionally, we use a rather than 1 to...
Problem 1. Show that the eigenvalue problem -X"(r) - XX(X), X(-) = X(L),X'(-) = X(L) has the following eigenvalues and eigenfunctions An - (92), X,(w) -- sin (7+), xy(x) = cos ("E") - - 0,1,2,...
4. (10 points) Let X be the normed linear space of all simple functions in L(E). Show that X is not a Banach space. 4. (10 points) Let X be the normed linear space of all simple functions in L(E). Show that X is not a Banach space.