Define the linear transformation T by T(x) = Ax. Find ker(7), nullity(7), range(7), and rank(7). 3 3 3 -3 (a) ker(T) A = (b) nullity (T) (d) range (T) R O {(t, 3t): t is any real number} O {(-t, t): t is any real number} O {(3t, t): t is any real number} O R² rank (T)
Define the linear transformation T by T(x) = Ax. Find ker(7), nullity(7), range(7), and rank(7). 3 3 3 -3 (a) ker(T) A = (b) nullity (T) (d) range (T) R O {(t, 3t): t is any real number} O {(-t, t): t is any real number} O {(3t, t): 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
Problem 1RQ
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![Define the linear transformation T by T(x) = Ax. Find ker(7), nullity(7), range(7), and rank(T).
3 3
3-3
A =
(a)
ker(T)
(b) nullity (T)
(c) range(T)
R
{(t, 3t): t is any real number}
O {(-t, t): t is any real number}
{(3t, t): t is any real number}
R²
(d)
rank (T)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F678fef96-64be-4096-a74a-c4eb0a405ee7%2F609174d1-fdbb-4ee8-876f-2a1f0108a431%2Fh7vuhym_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Define the linear transformation T by T(x) = Ax. Find ker(7), nullity(7), range(7), and rank(T).
3 3
3-3
A =
(a)
ker(T)
(b) nullity (T)
(c) range(T)
R
{(t, 3t): t is any real number}
O {(-t, t): t is any real number}
{(3t, t): t is any real number}
R²
(d)
rank (T)
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