Define the linear transformation T by T(x) = Ax. Find ker(T), nullity(T), range(T), and rank(T). 8 -8 A = 8 (a) ker(T) { (b) nullity(T) (c) range(T) O {(t, 8t): t is any real number} R O {(8t, t): t is any real number} O {(-t, t): t is any real number} R2 (d) rank(T)
Define the linear transformation T by T(x) = Ax. Find ker(T), nullity(T), range(T), and rank(T). 8 -8 A = 8 (a) ker(T) { (b) nullity(T) (c) range(T) O {(t, 8t): t is any real number} R O {(8t, t): t is any real number} O {(-t, t): t is any real number} R2 (d) rank(T)
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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Transcribed Image Text:Define the linear transformation T by T(x) = Ax. Find ker(T), nullity(T), range(T), and rank(T).
8 -8
A =
8
8
(a) ker(T)
(b) nullity(T)
(c) range(T)
O {(t, 8t): t is any real number}
R
{(8t, t): t is any real number}
{(-t, t): t is any real number}
O R2
(d) rank(7)
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