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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
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)
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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