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
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: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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