e linear operator defined by of the range of L: of the kernel of L: L(x) = ce of R³ spanned by 21e₁ and 13e2+ 13e3. Find the dimension of L(S):
e linear operator defined by of the range of L: of the kernel of L: L(x) = ce of R³ spanned by 21e₁ and 13e2+ 13e3. Find the dimension of L(S):
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:Let L : R³ →→ R³ be the linear operator defined by
(a) Find the dimension of the range of L:
(b) Find the dimension of the kernel of L:
L(x)=
(c) Let S be the subspace of R³ spanned by 21e₁ and 13e2+ 13e3. Find the dimension of L(S):
[7x₁+30x27x3
15x2
21x₁ - 21x3
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