(c) Show that if a span{b₁,b2, ..., b;} then bib{T bi bi (0.0.3) Hint: You can prove the contrapositive of the original proposition, and write vector a as linear combination of c and bk. c=a- i=1 a & span{b₁,b2, ..., bj}. (d) Show that in part (c) we also have that {b₁,b2, ..., bj, a} are linearly indepen- dent, providing a basis for a span of dimension j+ 1.

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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(c) Show that if a & span{b₁,b2, ..., b;} then
bib, T
j
c=a-
(0.0.3)
Hint: You can prove the contrapositive of the original proposition, and write
vector a as linear combination of c and bk.
i=1
-a & span{b₁,b2, ..., bj}.
bi bi
(d) Show that in part (c) we also have that {b1,b2, ..., bj, a} are linearly indepen-
dent, providing a basis for a span of dimension j+ 1.
Transcribed Image Text:(c) Show that if a & span{b₁,b2, ..., b;} then bib, T j c=a- (0.0.3) Hint: You can prove the contrapositive of the original proposition, and write vector a as linear combination of c and bk. i=1 -a & span{b₁,b2, ..., bj}. bi bi (d) Show that in part (c) we also have that {b1,b2, ..., bj, a} are linearly indepen- dent, providing a basis for a span of dimension j+ 1.
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