Let T : R3 → R³ be the linear mapping that projects a vector v into the yz-plane.Then, the image and the kernel of T are:a) Im(T) = {(x; y; 0)| x,y e R} and Ker(T) = {(0; 0; z)| z e R}b) Im(T) = {(x; 0; z)| x,z e R} and Ker(T) = {(0; y; 0)| y e R}c) Im(T) = {(0; y; z)| y,z e R} and Ker(T) = {(x; 0; 0)| x e R}d) Im(T) = {(x; y; z)| x, y e R} and Ker(T) = {(0; 0; 0)}O a)b)c)O d)e) None of the choices

Answered: Image /qna-images/answer/261aa1bd-3acb-4ffc-b9ce-e7d5beec2548.jpg

Let T' : R³ → R³ be the linear mapping that projects a vector v into the yz-p Then, the image and the kernel of T are: a) Im(T) = {(x; y; 0)| x, y e R} and Ker(T) = {(0; 0; z)| z e R} %3D b) Im(T) = {(x; 0; z)| x, z e R} and Ker(T) = {(0; y; 0)| y e R} c) Im(T) = {(0; y; z)| y,z e R} and Ker(T) = {(x; 0; 0)| x e R} d) Im(T) = {(x; y; z)| x, y e R} and Ker(T) = {(0; 0; 0)} %3D

Let T' : R³ → R³ be the linear mapping that projects a vector v into the yz-p Then, the image and the kernel of T are: a) Im(T) = {(x; y; 0)| x, y e R} and Ker(T) = {(0; 0; z)| z e R} %3D b) Im(T) = {(x; 0; z)| x, z e R} and Ker(T) = {(0; y; 0)| y e R} c) Im(T) = {(0; y; z)| y,z e R} and Ker(T) = {(x; 0; 0)| x e R} d) Im(T) = {(x; y; z)| x, y e R} and Ker(T) = {(0; 0; 0)} %3D

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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