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false? ? 1. If {V1, V2, V3} is an orthogonal basis for W, then multiplying V3 by a non-zero scalar c gives a new orthogonal basis {V1, V2, CV3}. ? Are the following statements true or 2. The best approximation to y by elements of a subspace W is given by the vector y - projw (y). ? ? have u. v = -v. u. 3. For all vectors u, v E R", we 4. If W is a subspace of R" and if v is in both W and W, then v must be the zero vector.

false? ? 1. If {V1, V2, V3} is an orthogonal basis for W, then multiplying V3 by a non-zero scalar c gives a new orthogonal basis {V1, V2, CV3}. ? Are the following statements true or 2. The best approximation to y by elements of a subspace W is given by the vector y - projw (y). ? ? have u. v = -v. u. 3. For all vectors u, v E R", we 4. If W is a subspace of R" and if v is in both W and W, then v must be the zero vector.

Advanced Engineering Mathematics
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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Problem 11. false? ? 1. If {V1, V2, V3} is an orthogonal basis for W, then multiplying V3 by a non-zero scalar c gives a new orthogonal basis {V₁, V2, CV3}. ? ? elements of a subspace W is given by the vector y - projw (y). Are the following statements true or ? î 2. The best approximation to y by ? have u v= -V. u. 3. For all vectors u, v E R", we n 4. If W is a subspace of R" and if v is in both W and W, then v must be the zero vector. 5. For any scalar c, and vectors u, v € R", we have u. (cv) = c(uv).
Transcribed Image Text:Problem 11. false? ? 1. If {V1, V2, V3} is an orthogonal basis for W, then multiplying V3 by a non-zero scalar c gives a new orthogonal basis {V₁, V2, CV3}. ? ? elements of a subspace W is given by the vector y - projw (y). Are the following statements true or ? î 2. The best approximation to y by ? have u v= -V. u. 3. For all vectors u, v E R", we n 4. If W is a subspace of R" and if v is in both W and W, then v must be the zero vector. 5. For any scalar c, and vectors u, v € R", we have u. (cv) = c(uv).
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