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Problem 2. Vectors V₁ = (4,6,7), V₂ = (0,1,1) and V3 = (0,1,2) form a basis for the vector space R³. Vectors u₁ = (1,1,1), u₂ = (1,2,2) and u3 = (2,3,4) form another basis for R³. (i) Find the transition matrix from the standard basis e₁,e2, es to the ordered basis u₁, U2, U3- (ii) Find the transition matrix from the ordered basis V₁, V₂, V3 to the ordered basis u₁, U₂, U3- (iii) Find coordinates of the vector w = 2v₁ + 3v₂ − 4v3 relative to the basis V₁, V2, V3- coordinates of w relative to the basis u₁, U₂, U3, and coordinates of w relative to the standard basis.

Problem 2. Vectors V₁ = (4,6,7), V₂ = (0,1,1) and V3 = (0,1,2) form a basis for the vector space R³. Vectors u₁ = (1,1,1), u₂ = (1,2,2) and u3 = (2,3,4) form another basis for R³. (i) Find the transition matrix from the standard basis e₁,e2, es to the ordered basis u₁, U2, U3- (ii) Find the transition matrix from the ordered basis V₁, V₂, V3 to the ordered basis u₁, U₂, U3- (iii) Find coordinates of the vector w = 2v₁ + 3v₂ − 4v3 relative to the basis V₁, V2, V3- coordinates of w relative to the basis u₁, U₂, U3, and coordinates of w relative to the standard basis.

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 6AEXP
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Problem 2. Vectors V₁ = (4,6,7), V₂ = (0,1,1) and V3 = (0,1,2) form a basis for the vector space R³. Vectors u₁ = (1, 1, 1), u₂ = (1,2,2) and u3 = (2,3,4) form another basis for R³. (i) Find the transition matrix from the standard basis e₁,e2, es to the ordered basis u₁, U2, U3. (ii) Find the transition matrix from the ordered basis V₁, V2, V3 to the ordered basis u₁, U₂, U3. (iii) Find coordinates of the vector w = 2v₁ + 3V₂ 4v3 relative to the basis V₁, V2, V3, coordinates of w relative to the basis u₁, U₂, U3, and coordinates of w relative to the standard basis.
Transcribed Image Text:Problem 2. Vectors V₁ = (4,6,7), V₂ = (0,1,1) and V3 = (0,1,2) form a basis for the vector space R³. Vectors u₁ = (1, 1, 1), u₂ = (1,2,2) and u3 = (2,3,4) form another basis for R³. (i) Find the transition matrix from the standard basis e₁,e2, es to the ordered basis u₁, U2, U3. (ii) Find the transition matrix from the ordered basis V₁, V2, V3 to the ordered basis u₁, U₂, U3. (iii) Find coordinates of the vector w = 2v₁ + 3V₂ 4v3 relative to the basis V₁, V2, V3, coordinates of w relative to the basis u₁, U₂, U3, and coordinates of w relative to the standard basis.
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