THEOREM 11.3.7 Let a be a real number. If an → L and bn → M, then (i) an+bn → L+M, (ii) aan → a L, If, in addition, M0 and each b₁ = 0, then 1 (iv) bn ← 1 and M (v) (iii) anbn → LM. an L →> bn M
THEOREM 11.3.7 Let a be a real number. If an → L and bn → M, then (i) an+bn → L+M, (ii) aan → a L, If, in addition, M0 and each b₁ = 0, then 1 (iv) bn ← 1 and M (v) (iii) anbn → LM. an L →> bn M
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 11AEXP
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Explain the key points of 11.3.7

Transcribed Image Text:THEOREM 11.3.7
Let a be a real number. If an → L and bn → M, then
(i) an+bn
→ L+M,
(ii) aan → a L,
If, in addition, M0 and each b₁ = 0, then
1
(iv)
bn
←
1
and
M
(v)
(iii) anbn
→ LM.
an
L
→>
bn M
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