Let -{-} W₁ = span be subspaces of R³. (a) Show that W₁ + W₂ = R³. (b) What are: dim(W₁ + W₂), and W₂ -----} {B} = span dim(W₁), dim(W₂), and dim(W₁) + dim(W₂)?
Let -{-} W₁ = span be subspaces of R³. (a) Show that W₁ + W₂ = R³. (b) What are: dim(W₁ + W₂), and W₂ -----} {B} = span dim(W₁), dim(W₂), and dim(W₁) + dim(W₂)?
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
{0·0}
W₁ = span
be subspaces of R³.
(a) Show that W₁ + W₂ = R³.
(b) What are:
and
-{0·0)
{D. B}
W₂ = span
dim(W₁ + W₂), dim(W₁), dim(W₂), and
dim(W₁) + dim(W₂)?
(c) Does dim (W₁ + W₂) = dim(W₁) + dim(W₂)? Does this contradict the previous problem?
Why or why not?
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