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Do the given vectors form an orthogonal basis for R3? 1 3 2 , u2 u3 Yes, the given set does form an orthogonal basis for R3. No, the given set does not form an orthogonal basis for R. You are given the theorem below. Let {u,, u, ..., u} be an orthogonal basis for a subspace w of R" and let v be any vector in W. Then the unique scalars C, such that .... v = cu, + + Cuk are given by for i = 1, ..., k. U.. U Use the theorem to express v as a linear combination of the above basis vectors. Give the coordinate vector [v], of v with respect to the basis B = {u,, u,, uz} of R. 1 v = 1 1 [v] = B.

Do the given vectors form an orthogonal basis for R3? 1 3 2 , u2 u3 Yes, the given set does form an orthogonal basis for R3. No, the given set does not form an orthogonal basis for R. You are given the theorem below. Let {u,, u, ..., u} be an orthogonal basis for a subspace w of R" and let v be any vector in W. Then the unique scalars C, such that .... v = cu, + + Cuk are given by for i = 1, ..., k. U.. U Use the theorem to express v as a linear combination of the above basis vectors. Give the coordinate vector [v], of v with respect to the basis B = {u,, u,, uz} of R. 1 v = 1 1 [v] = B.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 1AEXP
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Do the given vectors form an orthogonal basis for R3? 1 3 2 u, = u3 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 {u,, u, ..., u} be an orthogonal basis for a subspace w of R" and let v be any vector in W. Then the unique scalars C, such that .... v = c,u, + + Cuk are given by C, = for i = 1, ..., k. U.. U Use the theorem to express v as a linear combination of the above basis vectors. Give the coordinate vector [v], of v with respect to the basis B = {u,, u,, uz} of R. 1 v = 1 [v] = B.
Transcribed Image Text:Do the given vectors form an orthogonal basis for R3? 1 3 2 u, = u3 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 {u,, u, ..., u} be an orthogonal basis for a subspace w of R" and let v be any vector in W. Then the unique scalars C, such that .... v = c,u, + + Cuk are given by C, = for i = 1, ..., k. U.. U Use the theorem to express v as a linear combination of the above basis vectors. Give the coordinate vector [v], of v with respect to the basis B = {u,, u,, uz} of R. 1 v = 1 [v] = B.
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