b. Indicate whether any of the relations R, Sand T8. Let A = {2, 4} and B = {1, 3, 5} and define relations U, V and W from A to B as follows:%3DFor all (x, y) E A× B,(x, y) EU means that y -x > 2.(x, y) E V means that y - 1=W = {(2,5), (4, 1), (2,3)}.a. Draw arrow diagrams for U, Vand W.b. Indicate whether any of the relations U, Vand W are functions.%3D9 a Find all relations from {0, 1} to {1}.

Answered: 8. Let A = {2, 4} and B= {1, 3, 5} and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4.4. Suppose that u = (1,3) and v = (3, 1). (a) Sketch the points tu + v, ļu + v, and u + tv. (b) Draw the line of all linear combinations cu + dv with c+ d = 1. (c) Sketch u+v and u+v. Draw the line of all linear combinations си + сv. (d) Shade all combinations cu + dv for 0 0 and d > 0.
4. Explain why the two planes P₁: =(2,5,3)+(2,-1,-3) +(1,0,-1), s,/€ R, and P₂: r 7=(4,4,0) +(2,-1,3)+(-1,2,3),,/€ R are distinct.
8. Decide which of the following sets are linearly independent in R. Justify your answer in each case. (a) X₁ = {(1,0), (0, 1)} CR² (b) X₂ = {(1,0), (2,0)} CR² (c) X3 = {(-1,0), (0,0)} CR² (d) X₁ = {(1,0), (0, 1), (1, 1)} CR² (e) X5 = {(1,0,0), (0, 1, 0), (1, 1, 1)} CR³ (f) X6 = {(1,0,0), (0, 1, 0), (1, 1, 1), (-1,0,1)} CR³ (g) X7 = {(0, 0, 0), (0, 1, 0), (1, 1, 1), (-1,0,1)} CR³ (h) Xs = {(0, 1, 0), (1,1,1)} CR³ (i) X9 = {(4,3,0,0), (0, 0, 1, 1), (0, 0, 0, 1), (1, 0, 0, 1), (0, 1, 0, 1)} CR¹ (j) X10 = {(1,2,0,0), (0, 2, 3,0), (0, 0, -1, 1)} CR¹
6.1.4 Let A = [1,3], B = [2,4] and C = [2,3]. Prove or disprove that (Ах В)n (В х А) — СхС. C x Hint: Draw the sets A x B, B × A and C x C in the Cartesian plane. The picture will give you a hint on whether or not the statement is true, but it does not constitute a proof.
Given the lines L1 and L2: L1: (x,Y.z)=(-4,6,-2)+t(5,4,3), with tER. www L2: (x,V.z)=(7,16,6)+s(6,6,5), with sER. Consider the following statements about L1 and L2: I. The point P=(1,10,1) is a point of intersection of both lines. II. There does not exist a plane containing both straight lines. Of these, with certainty, which are true? a) None b) I AND II c) I d) II
28. Determine the point of intersection between the following pair of lines ở = (5,1,7) +s(2,0,5), s€R r = (-1,-1,3)+t(4,2,−1),t€R
{(а, 1), (ь, 3), (с, 4), (а, 1), (а, 2)} dan Rz {(w, 2), (w, 4), (y, 1), (z, 4)}. Determine Given two relations R1 R1 x R2.
For what value of x will make {(4,6), (8,10), (x-3, 21). (17,19)} satisfy the relation y = x + 2? А. 12 В. 22 С. 19 D. 25

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8. Let A = {2, 4} and B= {1, 3, 5} and define relations U, V For all (x, y) E A × B, (x, y) EU means that y-x > 2. (x, y) E V means that y - 1 = W = {(2,5), (4, 1), (2,3)}. a. Draw arrow diagrams for U, Vand W. %3D