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Let T: R4 → R3 be the linear transformation represented by T(x) = Ax, where %3D 1 -2 2 0 A = 1 1 3 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.

Let T: R4 → R3 be the linear transformation represented by T(x) = Ax, where %3D 1 -2 2 0 A = 1 1 3 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.

Advanced Engineering Mathematics
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: R4 → R3 be the linear transformation represented by T(x) = Ax, where 1 -2 2 0 A = 1 1 3 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 not one-to-one since the rank(T) # {0}. 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}. O Tis one-to-one since the ker(T) + {}. (e) Is T onto? Explain. O Tis not onto since the rank(T) is equal to the dimension of the range. O Tis not onto since the rank(T) is not equal to the dimension of the domain. O Tis onto since the rank(T) is equal to the dimension of the domain. O Tis not onto since the rank(T) is not equal to the dimension of the range. O Tis onto since the rank(T) is equal to the dimension of the range. (f) Is T an isomorphism? Explain. (Select all that apply.) 9 Tis an isomorphism since it is one-to-one and onto. 9 Tis not an isomorphism since it is not one-to-one. OTis not an isomorphism since it is not onto. Neod Hein? Read It e Type here to search
Transcribed Image Text:Let T: R4 → R3 be the linear transformation represented by T(x) = Ax, where 1 -2 2 0 A = 1 1 3 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 not one-to-one since the rank(T) # {0}. 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}. O Tis one-to-one since the ker(T) + {}. (e) Is T onto? Explain. O Tis not onto since the rank(T) is equal to the dimension of the range. O Tis not onto since the rank(T) is not equal to the dimension of the domain. O Tis onto since the rank(T) is equal to the dimension of the domain. O Tis not onto since the rank(T) is not equal to the dimension of the range. O Tis onto since the rank(T) is equal to the dimension of the range. (f) Is T an isomorphism? Explain. (Select all that apply.) 9 Tis an isomorphism since it is one-to-one and onto. 9 Tis not an isomorphism since it is not one-to-one. OTis not an isomorphism since it is not onto. Neod Hein? Read It e Type here to search
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