Question

Assume A in Rd is an open set. What can you say about the set Pe1(A), where Pe1(A) is an orthogonal projection of A onto the subspace orthogonal to the first basis vector e1, i.e. Pe1(A) = {(0, a2, ..., ad) : (a1, a2, ..., ad) ∈ A}? Note that here we can ask two questions: 1. Is Pe1(A) an open set in Rd? 2. Is Pe1(A) an open set in the subspace orthogonal to the first basis vector e1?

Name: assume a in rd is an open set what can you say about the set pe1a where pe1a is an orthogonal projection of a onto the subspace orthogonal to the first basis vector e1 ie pe1a 0 a2 ad a1 a2 93627
Uploaded: 2023-05-24T09:38:59-08:00
Duration: 2 min 49 s
Channel: Madhur L
Description: assume a in rd is an open set what can you say about the set pe1a where pe1a is an orthogonal projection of a onto the subspace orthogonal to the first basis vector e1 ie pe1a 0 a2 ad a1 a2 93627

          Assume A in Rd is an open set. What can you say about the set Pe1(A), where Pe1(A) is an orthogonal projection of A onto the subspace orthogonal to the first basis vector e1, i.e. Pe1(A) = {(0, a2, ..., ad) : (a1, a2, ..., ad) ∈ A}? 

Note that here we can ask two questions: 
1. Is Pe1(A) an open set in Rd? 
2. Is Pe1(A) an open set in the subspace orthogonal to the first basis vector e1?

Added by Gary P.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Madhur L

05/24/2023

Step 1

An open set in Rd is a set that contains a neighborhood around each of its points. In other words, for every point x in the set, there exists a positive radius r such that the ball B(x, r) = {y : ||y - x|| < r} is completely contained in the set. Show more…

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Assume A in Rd is an open set. What can you say about the set Pe1(A), where Pe1(A) is an orthogonal projection of A onto the subspace orthogonal to the first basis vector e1, i.e. Pe1(A) = {(0, a2, ..., ad) : (a1, a2, ..., ad) ∈ A}? Note that here we can ask two questions: 1. Is Pe1(A) an open set in Rd? 2. Is Pe1(A) an open set in the subspace orthogonal to the first basis vector e1?