Please write neatly and legibly. Please show all work.
Please write neatly and legibly. Please show all work. 1. Recall that given a basis, the...
Please solve all in detail! 7. Recall that if o E Sn then P, is the nxn "permutation matrix” satisfying Col;(P.) = Co(j) for j = 1,...,n. (See the Tutorial notes for Feb. 24 for more information.) (a) Prove that if o, T E Sn then P.P, = Por. (Hint: it suffices to prove Col;(P.P.) = Col;(Por) for all j. Use the general fact that Col;(A) = Ae..] (b) Suppose o E Sn given in cycle notation is o =...
Q2) Please show all working out neatly. If the answer is neat and correct I will upvote. Thanks! :) 2. Prove (without using Theorem 2.5) that if A and B are symmetric matrices, A + B is idempotent and AB = BA = 0, then both A and B are idempotent. (Hint: Use Theorem 2.4. Then derive two relations between the diagonalisations of A and B.) Theorem 2.4 Let A1, A2, ..., Am be a collection of symmetric k x...
Write solutions legibly, and show all work. Walk the reader through your thought process, using English words when necessary. 1. Recall question 2 of the previous homework – We draw 6 cards from a 52 card deck and let X = the number of heart cards drawn. You already found the pmf back then. You’re allowed to use it here without re-deriving it. a. What is the expected value of X? b. What is the variance of X? What is...
Directions: Do all work in this booklet. To receive credit, write legibly and show all work. Br work. You must do all problems by the methods taught in this course and that iëfly explain your have been covered to date (sections 2.1-2.6). All answers are to be exact expressions, i.e. V3, not 1.732 and r, not 3.1416,unless otherwise specified, and appropriately simplified. CIRCLE your answers. 1. A metal products manufacturer acquires a new heat-treating machine for $106. The machine is...
(a) Find the LU decomposition for A and use it to write A as a sum of simple matrices. (b) Find the basis of the null space of A. (c) (d) Please explain every step clearly and legibly. 101 101 [X1 , X2, X3, X4]T Show that the problem Ax = b with b = [1,-1, 2]T, X is consistent. Using the information in parts (a-d), find a solution such that We were unable to transcribe this image 101 101...
please show all work, even trivial steps. Here are definitions if needed. do not write in script thank you! 4. Letf: R2 → R2, by f(x,y) = (x-ey,xy). a. Find Df (2,0). b. Find DF-1(f (2,0)) Inverse Function Theorem: Suppose that f:R" → R" is continuously differentiable in an open set containing a and det(Df(a)) = 0, then there is an open set, V, containing a and an open set, W, containing f(a) such that f:V W has a continuous...
Please write neatly and clearly, show all work. Thank you! (I've been stumped for awhile) (1 point) Find the smallest positive integer x that solves the congruence: 11x = 4 (mod 68) x = (Hint: From running the Euclidean algorithm forwards and backwards we get 1 = s(11) + +(68). Find s and use it to solve the congruence.)
Please show all your work and write neatly please! Thank you guys! ?? Solve the following problems. The activation energy for the reaction below equals 1.0 x 105 J/mol. Given k 2.5 x 103 sec1 at 332 K, find k at 375 K. 1. N20s (g)-2NO (g) + 0a(g) Based on information in problem 1, find the temperature at which k is twice as large as it is at 332K. 2.
Problem 1: Recall that the Chebyshev nodes 20, 21, ...,.are determined on the interval (-1,1) as the zeros of Tn+1(x) cos((n + 1) arccos(x)) and are given by 2; +17 Tj = COS , j = 0,1,...n. n+1 2 Consider now interpolating the function f(x) = 1/(1 + x2) on the interval (-5,5). We have seen in lecture that if equispaced nodes are used, the error grows unbound- edly as more points are used. The purpose of this problem is...