Do the given vectors form an orthogonal basis for R³? [³] V1 = are given by [w] = B -2 Yes, the given set does form an orthogonal basis for R³. No, the given set does not form an orthogonal basis for R³. You are given the theorem below. Let (V₁, V₂ 2 v> be an orthogonal basis for a subspace W of R" and let w be any vector in W. Then the unique scalars c₁, W=C₁V₁ + + CK k W W = v₂ = ¡'Vi V3 = U Use the theorem to express w as a linear combination of the above basis vectors. Give the coordinate vector [w] of w with respect to the basis 8 = for i=1, k. Ck such that (V₁, V₂, V3) of R³.
Do the given vectors form an orthogonal basis for R³? [³] V1 = are given by [w] = B -2 Yes, the given set does form an orthogonal basis for R³. No, the given set does not form an orthogonal basis for R³. You are given the theorem below. Let (V₁, V₂ 2 v> be an orthogonal basis for a subspace W of R" and let w be any vector in W. Then the unique scalars c₁, W=C₁V₁ + + CK k W W = v₂ = ¡'Vi V3 = U Use the theorem to express w as a linear combination of the above basis vectors. Give the coordinate vector [w] of w with respect to the basis 8 = for i=1, k. Ck such that (V₁, V₂, V3) of R³.
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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![Do the given vectors form an orthogonal basis for R³?
[³]
V1 =
are given by
[w] =
B
-2
Yes, the given set does form an orthogonal basis for R³.
No, the given set does not form an orthogonal basis for R³.
You are given the theorem below.
Let (V₁, V₂
2
v> be an orthogonal basis for a subspace W of R" and let w be any vector in W. Then the unique scalars c₁,
W=C₁V₁ +
+ CK k
W
W =
v₂ =
¡'Vi
V3 =
U
Use the theorem to express w as a linear combination of the above basis vectors. Give the coordinate vector [w] of w with respect to the basis 8 =
(V1, V₂, V3) of R³.
for i=1, k.
Ck such that](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67ad69fc-d7b2-4082-8b18-7ae4b62544b8%2F2ea9fc90-3289-44b9-96c2-18f83dcb0ea7%2Fwruyc9j_processed.png&w=3840&q=75)
Transcribed Image Text:Do the given vectors form an orthogonal basis for R³?
[³]
V1 =
are given by
[w] =
B
-2
Yes, the given set does form an orthogonal basis for R³.
No, the given set does not form an orthogonal basis for R³.
You are given the theorem below.
Let (V₁, V₂
2
v> be an orthogonal basis for a subspace W of R" and let w be any vector in W. Then the unique scalars c₁,
W=C₁V₁ +
+ CK k
W
W =
v₂ =
¡'Vi
V3 =
U
Use the theorem to express w as a linear combination of the above basis vectors. Give the coordinate vector [w] of w with respect to the basis 8 =
(V1, V₂, V3) of R³.
for i=1, k.
Ck such that
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