? 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}. ? 2. If y = Z₁ + Z2, where Z₁ is in a subspace W and Z2 is in W-, then z₁ must be the orthogonal projection of y onto W. ? 3. If W = Span{x₁, X2, X3} with {x₁, X2, X3} inearly independent, and if {V₁, V2, V3} is an orthogonal set in W consisting of non-zero vectors, then {V₁, V2, V3} is an orthogonal basis for W. ? î 4. If ||u||² + ||v||² = ||u - v||², then the vectors u and v are orthogonal. ? ||cv|| = c||v||. 5. For any scalar c and any vector v € R",
? 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}. ? 2. If y = Z₁ + Z2, where Z₁ is in a subspace W and Z2 is in W-, then z₁ must be the orthogonal projection of y onto W. ? 3. If W = Span{x₁, X2, X3} with {x₁, X2, X3} inearly independent, and if {V₁, V2, V3} is an orthogonal set in W consisting of non-zero vectors, then {V₁, V2, V3} is an orthogonal basis for W. ? î 4. If ||u||² + ||v||² = ||u - v||², then the vectors u and v are orthogonal. ? ||cv|| = c||v||. 5. For any scalar c and any vector v € R",
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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True or false
Transcribed Image Text:?
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}.
?
?
2. If y =
Z₂ is in W, then Z₁ must be the orthogonal projection of y onto
W.
?
= Z1 + Z₂, where Z₁ is in a subspace W and
Span{X₁, X2, X3} with {X1, X2, X3}
linearly independent, and if {V₁, V2, V3} is an orthogonal set in W
consisting of non-zero vectors, then {V₁, V2, V3} is an orthogonal
basis for W.
3. If W
=
4. If ||u||² + ||v||² = ||u – v||², then the vectors u
?
||cv|| = c||v||.
and v are orthogonal.
5. For any scalar c and any vector v ER",
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