Define the linear transformation T by T(x) = Ax. Find ker(7), nullity(7), range(T), and rank(T). A = 4- [6. (a) 6 6-6 ker(T) (b) nullity (T) (c) range(T) O {(6t, t): t is any real number} {(-t, t): t is any real number} (d) OR O {(t, 6t): t is any real number} O R² rank (T)

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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Define the linear transformation T by T(x) = Ax. Find ker(7), nullity(7), range(T), and rank(T).
A =
4- [6.
(a)
6
6-6
ker(T)
(b) nullity (T)
(c) range(T)
O {(6t, t): t is any real number}
{(-t, t): t is any real number}
(d)
OR
O {(t, 6t): t is any real number}
O R²
rank (T)
Transcribed Image Text:Define the linear transformation T by T(x) = Ax. Find ker(7), nullity(7), range(T), and rank(T). A = 4- [6. (a) 6 6-6 ker(T) (b) nullity (T) (c) range(T) O {(6t, t): t is any real number} {(-t, t): t is any real number} (d) OR O {(t, 6t): t is any real number} O R² rank (T)
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