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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Transcribed Image Text: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
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