Let T: RS → R³ be the linear transformation by T(v) = Av, where 3 2 1 235 00 21 2 0 (a) Find the ker(7). (b) Find the nullity(T). (c) Find the range(T). (d) Find the rank(7). (e) Is T one-to-one? Explain. (f) Is T onto? Explain. (g) Is T an isomorphism? Explain. A=

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: RS R³ be the linear transformation by T(v) = Av, where
-1
3 2 1
2 3 500
21 2
(a) Find the ker(7).
(b) Find the nullity(T).
(c) Find the range(T).
(d) Find the rank(T).
(e) Is T one-to-one? Explain.
(f) Is T onto? Explain.
(g) Is T an isomorphism? Explain.
A=
00
0
Transcribed Image Text:Let T: RS R³ be the linear transformation by T(v) = Av, where -1 3 2 1 2 3 500 21 2 (a) Find the ker(7). (b) Find the nullity(T). (c) Find the range(T). (d) Find the rank(T). (e) Is T one-to-one? Explain. (f) Is T onto? Explain. (g) Is T an isomorphism? Explain. A= 00 0
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