Let T: R3 → R? be a linear transformation such that T(v) = A(v), where 1 2 0 0 1 0 0 1 A = 1 (a) Find the dimension of the domain (b) Find the kernel of T and its the dimension. (c) Find the range of T and its dimension. (d) Is T one-to-one? Explain (e) Is T onto? Explain (f) Is T an isomorphism? Explain

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let T : R³ → R² be a linear transformation such that T(v) = A(v), where
1 2 0
0 1
0 0 1
A
1
(a) Find the dimension of the domain
(b) Find the kernel of T and its the dimension.
(c) Find the range of T and its dimension.
(d) Is T one-to-one? Explain
(e) Is T onto? Explain
(f) Is T an isomorphism? Explain
Transcribed Image Text:Let T : R³ → R² be a linear transformation such that T(v) = A(v), where 1 2 0 0 1 0 0 1 A 1 (a) Find the dimension of the domain (b) Find the kernel of T and its the dimension. (c) Find the range of T and its dimension. (d) Is T one-to-one? Explain (e) Is T onto? Explain (f) Is T an isomorphism? Explain
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