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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 8E
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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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