Let T: R* - R be the linear transformation represented by T(x) = Ax, where 1 -2 1 0 A = 0 1 2 4 0 0 0 1] (a) Find the dimension of the domain. (b) Find the dimension of the range. (c) Find the dimension of the kernel. (d) Is T one-to-one? Explain. O Tis one-to-one since the ker(T) = {0}. O Tis not one-to-one since the ker(T) = {0}. O Tis not one-to-one since the ker(T) = (0}. Tis not one-to-one since the rank(T) = {0}. O Tis one-to-one since the ker(T) = {0}.
Let T: R* - R be the linear transformation represented by T(x) = Ax, where 1 -2 1 0 A = 0 1 2 4 0 0 0 1] (a) Find the dimension of the domain. (b) Find the dimension of the range. (c) Find the dimension of the kernel. (d) Is T one-to-one? Explain. O Tis one-to-one since the ker(T) = {0}. O Tis not one-to-one since the ker(T) = {0}. O Tis not one-to-one since the ker(T) = (0}. Tis not one-to-one since the rank(T) = {0}. O Tis one-to-one since the ker(T) = {0}.
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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![Let T: R* - R be the linear transformation represented by T(x) = Ax, where
1 -2 1 0
A = 0 1 2 4
0 0 0 1]
(a) Find the dimension of the domain.
(b) Find the dimension of the range.
(c) Find the dimension of the kernel.
(d) Is T one-to-one? Explain.
O Tis one-to-one since the ker(T) = {0}.
O Tis not one-to-one since the ker(T) = {0}.
O Tis not one-to-one since the ker(T) = (0}.
Tis not one-to-one since the rank(T) = {0}.
O Tis one-to-one since the ker(T) = {0}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b23f77c-9fbd-438b-9a66-8ea76821c63e%2F2a9620a9-3b5a-45be-b20c-d3fbf70d2ba6%2F6nplp3.jpeg&w=3840&q=75)
Transcribed Image Text:Let T: R* - R be the linear transformation represented by T(x) = Ax, where
1 -2 1 0
A = 0 1 2 4
0 0 0 1]
(a) Find the dimension of the domain.
(b) Find the dimension of the range.
(c) Find the dimension of the kernel.
(d) Is T one-to-one? Explain.
O Tis one-to-one since the ker(T) = {0}.
O Tis not one-to-one since the ker(T) = {0}.
O Tis not one-to-one since the ker(T) = (0}.
Tis not one-to-one since the rank(T) = {0}.
O Tis one-to-one since the ker(T) = {0}.
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