Define the linear transformation T by T(x) = Ax. Find ker(7), nullity(7), range(7), and rank(T). 9 -7 1 1 1 -1 ker(7) A = (a) (b) nullity (7) (c) range (7) O {(s, t, s 8t): s, t are any real number} R² O {(8s, 8t, st): s, t are any real number} O {(s, t, 0): s, t are any real number} O R³ (d) 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(7), and rank(7).
9 -7
1 1
1
-1
A =
(a) ker(T)
(b) nullity(T)
(c) range(7)
O {(s, t, s 8t): s, t are any real number}
R²
{(8s, 8t, s t): s, t are any real number}
O {(s, t, 0): s, t are any real number}
O R³
(d) rank(T)
Transcribed Image Text:Define the linear transformation T by T(x) = Ax. Find ker(7), nullity(7), range(7), and rank(7). 9 -7 1 1 1 -1 A = (a) ker(T) (b) nullity(T) (c) range(7) O {(s, t, s 8t): s, t are any real number} R² {(8s, 8t, s t): s, t are any real number} O {(s, t, 0): s, t are any real number} O R³ (d) rank(T)
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