Do the given vectors form an orthogonal basis for R32 v = v, = O Yes, the given set does form an orthogonal basis for R3. O No, the given set does not form an orthogonal basis for R3. You are given the theorem below. Let {v,, v,, ..., v} be an orthogonal basis for a subspace W of R" and let w be any vector in W. Then the unique scalars c,..., Cy such that w = c,v, + + CVk are given by C = for i = 1, ..., k. 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 B = (v,, v, v} of R W =
Do the given vectors form an orthogonal basis for R32 v = v, = O Yes, the given set does form an orthogonal basis for R3. O No, the given set does not form an orthogonal basis for R3. You are given the theorem below. Let {v,, v,, ..., v} be an orthogonal basis for a subspace W of R" and let w be any vector in W. Then the unique scalars c,..., Cy such that w = c,v, + + CVk are given by C = for i = 1, ..., k. 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 B = (v,, v, v} of R W =
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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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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![Do the given vectors form an orthogonal basis for R32
v,
v, =
V =
O Yes, the given set does form an orthogonal basis for R3.
O No, the given set does not form an orthogonal basis for R3.
You are given the theorem below.
Let {v,, v2,..., v} be an orthogonal basis for a subspace W of R" and let w be any vector in W. Then the unique scalars c,..,Cy such that
w = c,v, + · + CVK
are given by
for i = 1, ..., k.
%3D
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 B = {v,,v, v} of RS
w =
1
1.
wl, =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d923420-f505-4fd0-9391-bee01944e4b1%2F04cf17dd-8401-461a-9845-5fd1a4330b7b%2Fwcgkgyp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Do the given vectors form an orthogonal basis for R32
v,
v, =
V =
O Yes, the given set does form an orthogonal basis for R3.
O No, the given set does not form an orthogonal basis for R3.
You are given the theorem below.
Let {v,, v2,..., v} be an orthogonal basis for a subspace W of R" and let w be any vector in W. Then the unique scalars c,..,Cy such that
w = c,v, + · + CVK
are given by
for i = 1, ..., k.
%3D
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 B = {v,,v, v} of RS
w =
1
1.
wl, =
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