Define the linear transformation I by T(X) = Ax. Find ker(T), nullity(T), range(T), and rank(T). 0 -8 6 A = 16 O 17 (a) ker(7) (If there are an infinite number of solutions use t as your parameter.) {[ (b) nullity(T) (c) range(T) {(0, t): t is any real number} {(16s, 8t, 17s - 6t): s, t are any real number} {(s, 0): s is any real number} R3 R2 (d) rank(T)
Define the linear transformation I by T(X) = Ax. Find ker(T), nullity(T), range(T), and rank(T). 0 -8 6 A = 16 O 17 (a) ker(7) (If there are an infinite number of solutions use t as your parameter.) {[ (b) nullity(T) (c) range(T) {(0, t): t is any real number} {(16s, 8t, 17s - 6t): s, t are any real number} {(s, 0): s is any real number} R3 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).
O -8
A =
16
17
(a)
ker(T) (If there are an infinite number of solutions use t as your parameter.)
{[
}
(b) nullity(T)
(c) range(T)
O {(0, t): t is any real number}
{(16s, 8t, 17s - 6t): s, t are any real number}
O {(s, 0): s is any real number}
O R3
O R2
(d) rank(T)
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