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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 24EQ
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