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.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 10CM

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