-) Let dim(V) = n. Let T : V → V be a linear operator. Let W1, W2 C V e T-invariant subspaces. Suppose V = W1 ☺ W2. Let B1 = (w1,·, wk) be (Uk+1, · · · , Vn) be an ordered basis for W2. (Wi, · . , Wk, Vk+1; •• • , Un) is an ordered ... n ordered basis for W1 and let B2 By a previous homework problem, B asis for V. Prove that: A0 В where A: B[T|w,]8, and B =
-) Let dim(V) = n. Let T : V → V be a linear operator. Let W1, W2 C V e T-invariant subspaces. Suppose V = W1 ☺ W2. Let B1 = (w1,·, wk) be (Uk+1, · · · , Vn) be an ordered basis for W2. (Wi, · . , Wk, Vk+1; •• • , Un) is an ordered ... n ordered basis for W1 and let B2 By a previous homework problem, B asis for V. Prove that: A0 В where A: B[T|w,]8, and B =
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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please prove!
![2) Let dim(V)
be T-invariant subspaces. Suppose V = W1 W2. Let B1
an ordered basis for W1 and let B2 = (vk+1, · ·.
= n. Let T : V → V be a linear operator. Let W1, W2 CV
= (w1, ·.., wk) be
,Un) be an ordered basis for W2.
By a previous homework problem, B = (w1,·…· , Wk, Vk+1, ·.. , Vn) is an ordered
(W1,
basis for V. Prove that:
ГА
[T];
A0
В
where A
8,[T\w,]8, and B =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52ca9638-4007-484a-a3f1-9c4ab883b973%2Ffb202f3b-d67f-40d9-8a1e-4e96f8cce711%2Fb8clmc_processed.png&w=3840&q=75)
Transcribed Image Text:2) Let dim(V)
be T-invariant subspaces. Suppose V = W1 W2. Let B1
an ordered basis for W1 and let B2 = (vk+1, · ·.
= n. Let T : V → V be a linear operator. Let W1, W2 CV
= (w1, ·.., wk) be
,Un) be an ordered basis for W2.
By a previous homework problem, B = (w1,·…· , Wk, Vk+1, ·.. , Vn) is an ordered
(W1,
basis for V. Prove that:
ГА
[T];
A0
В
where A
8,[T\w,]8, and B =
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