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Let B={u1, U2, u3} and B = {V1, V2, V3} be bases for a vector space V, and let 3-15 P = 1 1 4 0 12 be the transition matrix from B' to B. Express U1, U2, U3 as linear combinations of V1, V2, V3. u₁ = ( )V₁+ ( )V2+( )V3 i U2 = ( )V1+ ( )v2+( )V3 i 43 = ( )v₁+( )v₂+( )V3

Let B={u1, U2, u3} and B = {V1, V2, V3} be bases for a vector space V, and let 3-15 P = 1 1 4 0 12 be the transition matrix from B' to B. Express U1, U2, U3 as linear combinations of V1, V2, V3. u₁ = ( )V₁+ ( )V2+( )V3 i U2 = ( )V1+ ( )v2+( )V3 i 43 = ( )v₁+( )v₂+( )V3

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 65E: Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector...
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Let B={u1, U2, u3} and B = {V1, V2, V3} be bases for a vector space V, and let 3-15 P = 1 1 4 0 12 be the transition matrix from B' to B. Express U1, U2, U3 as linear combinations of V1, V2, V3. u₁ = ( )V₁+ ( )V2+( )V3 i U2 = ( )V1+ ( )v2+( )V3 i 43 = ( )v₁+( )v₂+( )V3
Transcribed Image Text:Let B={u1, U2, u3} and B = {V1, V2, V3} be bases for a vector space V, and let 3-15 P = 1 1 4 0 12 be the transition matrix from B' to B. Express U1, U2, U3 as linear combinations of V1, V2, V3. u₁ = ( )V₁+ ( )V2+( )V3 i U2 = ( )V1+ ( )v2+( )V3 i 43 = ( )v₁+( )v₂+( )V3
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