(1 point) Match each linear system with one of the phase plane vector fields. 71 1....
(1 point) Match each linear system with one of the phase plane direction fields. (The blue lines are the arrow shafts, and the black dots are the arrow tips) ? 1. - ? 2 = ? 3. ?
11. Match each linear system with one of the phase plane direction fields. 1 -3 a. 2 3 1 3 b. _ 2 1 1 0 C. 0 3 1 d 0 2 y B L L 11. Match each linear system with one of the phase plane direction fields. 1 -3 a. 2 3 1 3 b. _ 2 1 1 0 C. 0 3 1 d 0 2 y B L L
**2 (1 point) Match each linear system with one of the phase plane direction fields. (The blue lines are the arrow shafts, and the black dots are the arrow tips.) D$ 1.59 = [- 11111!IN IIIIII +1+ Note: To solve this problem, you only need to compute eigenvalues. In fact, it is enough to just compute whether the eigenvalues are
Match each linear system with one of the phase plane direction fields. (The blue lines are the arrow shafts, and the black dots are the arrow tips.) 2 1. y' ܒ ܝܕ IS 3 ? 2.4"-16 y 3 1 1 ? 3. 3 ? 4.5' 3 5 В A 12 1 1 с D
Problem 9. PREVIEW ONLY -- ANSWERS NOT RECORDED (1 point) Match each linear system with one of the phase plane direction fields. (The blue lines are the arrow shafts, and the black dots are the arrow tips.) ? 1.7 -14 1 3 2 5 y 1 2. y 1. 1 3 А 111/ ? 3. U 1 3 2 2 1 - N1 . ? v 4.4 -3 0-2 y + 4 1 + II- IIII 11 + D Note:...
1. (20 points) Identify if the following vector fields are conservative. If there exists a vector field that is conservative, you must also find a potential function for that field. (a) F(x,y,z) = (x3 – xy +z)i + 2 (b) F(x,y,z) = (y+z)i + (x+z)j + (x+y)k (& +y +y-22) i + (- y2)k
(1 point) (a) Show that each of the vector fields F-4yi + 4x j, G-i ЗУ x2+y2 x?+yi J, and j are gradient vector fields on some domain (not necessarily the whole plane) x2+y2 by finding a potential function for each. For F, a potential function is f(x, y) - For G, a potential function is g(x, y) - For H, a potential function is h(x, y) (b) Find the line integrals of F, G, H around the curve C...
For each of the following vector fields, find its curl and determine if it is a gradient field. (1 point) For each of the following vector fields, find its curl and determine if it is a gradient field. (a) F = 5(xy + 22) + 10(x2 + y2) 7+ 10(x2 + y2) k. curl F = F ? (b) Ğ = 5yzi + (52z+z2) 7+ (5xy + 2yz) k: curl Ĝ = Ğ ? (c) H = (5xy + yz)...
(1 point) (a) Show that each of the vector fields F = 4yi + 4xj, G= x y zit vol y J, and ] = vertinant virtuaj are gradient vector fields on some domain (not necessarily the whole plane) by finding a potential function for each. For F, a potential function is f(x, y) = For G, a potential function is g(x, y) = For i, a potential function is h(x, y) = (b) Find the line integrals of F,...
Consider the system of linear ODES 1 (1) = 35 yj (1) - 16 y2 (1) – 26 yz (1), dy2 (1) = 30 yy (0) - 15 y2 (1) – 22 yz (1). di Y3 (1) = 36 y1 (1) - 16 yz (1) - 27 y3 (). (71 The system of equation written as y' (t) = Ay(t), where y(t) = 2(1) (a) Enter the matrix A in the box below. ab sin(a) f a 2 (-1) (-2)(-1...