Define the linear transformation T by T(x) = Ax. Find ker(T), nullity(T), range(T), and rank(T). 9 -7 A = 1 1 1 -1 (a) ker(T) -5,3, – 1 (b) nullity(T) (c) range(T) {(s, t, s - 8t): s, t are any real number} {(s, t, 0): s, t are any real number} {(8s, 8t, s - t): s, t are any real number} R3 R2 (d) rank(T)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Define the linear transformation T by T(x) = Ax. Find ker(T), nullity(T), range(T), and rank(T).
9 -7
A =
1
1
1 -1
(a)
ker(T)
-5,3, – 1
(b)
nullity(T)
(c) range(T)
{(s, t, s - 8t): s, t are any real number}
{(s, t, 0): s, t are any real number}
{(8s, 8t, s - t): s, t are any real number}
R3
R2
(d) rank(T)
Transcribed Image Text:Define the linear transformation T by T(x) = Ax. Find ker(T), nullity(T), range(T), and rank(T). 9 -7 A = 1 1 1 -1 (a) ker(T) -5,3, – 1 (b) nullity(T) (c) range(T) {(s, t, s - 8t): s, t are any real number} {(s, t, 0): s, t are any real number} {(8s, 8t, s - t): s, t are any real number} R3 R2 (d) rank(T)
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