9) Find the transformation from u, v space to x, y, z space that takes the triangle U = [(0,0), (1, to the triangle Т%3 [(1,0, —2), (-1,2,0), (1, 1, 2)] Consider T (U, V) (a^u + bjv + cq, azu + b2v + C2, a3u b3vc3) Obtain the transformation from u, v to x, y, z T (0,0) = (a1(0) + b(0) C1, a2(0) + b2(0) c2, a3(0) + b3(0) Т (0,0) %3D (с1. С2, Сз) C3) Т (0,0) 3D (1,0, —2) C1 1, c2 0, c3 = -2 c1, a2(1) + b2(0) + C2, a3(1) + b3(0) C3) T (1,0) = (a1(1) b,(0) T (1,0) = (a1 +c1, a2 C2, a3 +C3) T (1,0) -1,2,0) a, c1-1, a2 + C2 3D 2, аз + Сз — 0 a1 -2, a2 = 2, a3 = 2 T (0,1) = (a1(0) + b(1)C1,a2(0) + b2(1) c2, a3(0) + b3(1) C3) (b1ci, b2 + C2, b3 +C3) T (0,1) T (0,1) (1,1,2) b1 +c = 1, b2+c2= 1, b3C3 2 b1 0, b2 1, b3 = 4 : T(и, v) 3D (-2и + 1,2и + v, 2u + 4v — 2) .. 10) Using the transformation of Exercise 9, find the pullback of (у — 1) dydz + (у + z)dzdx- dxdy _

9) Find the transformation from u, v space to x, y, z space that takes the triangle U = [(0,0), (1, to the triangle Т%3 [(1,0, —2), (-1,2,0), (1, 1, 2)] Consider T (U, V) (a^u + bjv + cq, azu + b2v + C2, a3u b3vc3) Obtain the transformation from u, v to x, y, z T (0,0) = (a1(0) + b(0) C1, a2(0) + b2(0) c2, a3(0) + b3(0) Т (0,0) %3D (с1. С2, Сз) C3) Т (0,0) 3D (1,0, —2) C1 1, c2 0, c3 = -2 c1, a2(1) + b2(0) + C2, a3(1) + b3(0) C3) T (1,0) = (a1(1) b,(0) T (1,0) = (a1 +c1, a2 C2, a3 +C3) T (1,0) -1,2,0) a, c1-1, a2 + C2 3D 2, аз + Сз — 0 a1 -2, a2 = 2, a3 = 2 T (0,1) = (a1(0) + b(1)C1,a2(0) + b2(1) c2, a3(0) + b3(1) C3) (b1ci, b2 + C2, b3 +C3) T (0,1) T (0,1) (1,1,2) b1 +c = 1, b2+c2= 1, b3C3 2 b1 0, b2 1, b3 = 4 : T(и, v) 3D (-2и + 1,2и + v, 2u + 4v — 2) .. 10) Using the transformation of Exercise 9, find the pullback of (у — 1) dydz + (у + z)dzdx- dxdy _

Name: Hi , I need assistance with calc 4 question you told me to post under
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Description: Hi , I need assistance with calc 4 question you told me to post under advanced math instead. It's number 10 dealing w/ pullbacks referenceing number 9 which I have attached. Thanks 9) Find the transformation from u, v space to x, y, z space that take

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}

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