Let Wi and W2 be two two-dimensional subspaces of the linear space R³, that is dim W1 W = W1n W2 is a subspace of the dimension at least 1, that is dim W > 1. dim W2 = 2. Prove that the intersection of these two-dimensional spaces
Let Wi and W2 be two two-dimensional subspaces of the linear space R³, that is dim W1 W = W1n W2 is a subspace of the dimension at least 1, that is dim W > 1. dim W2 = 2. Prove that the intersection of these two-dimensional spaces
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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![5. Let W1 and W2 be two two-dimensional subspaces of the linear space R°, that is
dim W1
W = W1n W2 is a subspace of the dimension at least 1, that is dim W > 1.
= dim W2
2. Prove that the intersection of these two-dimensional spaces](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7abbf2d5-6ef3-489c-b2da-4d9327a88b2a%2Fcbed7a85-5fd4-4a8f-be66-991a8be6a299%2Fd1dlu08h_processed.png&w=3840&q=75)
Transcribed Image Text:5. Let W1 and W2 be two two-dimensional subspaces of the linear space R°, that is
dim W1
W = W1n W2 is a subspace of the dimension at least 1, that is dim W > 1.
= dim W2
2. Prove that the intersection of these two-dimensional spaces
Expert Solution
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Step 1
Given
and be the two-dimensional subspace of linear space .
And
let
therefore
where (field)
Hence is the subspace.
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