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4) Consider the following three vector spaces with corresponding basis: V₁ =R³ B₁ = {e₁,e2, e3} B₂ = {1, t, t²} V₂ =R[t]<2 1 V3 = M2x2 (R) B3 = - - ( ) ( ) ( ) ( ) 0 1 Now consider the following two linear transformations: T (₁) T(b)=a+b-ct + at² C S(a + a₁ + a₂t²) = ao-a₂ a1 ao + a₁ a2 (a) Compute [T] (b) Compute [S] (c) Compute [ST] and verify that [ST]B³ = [S]B³₂[T]B³²

4) Consider the following three vector spaces with corresponding basis: V₁ =R³ B₁ = {e₁,e2, e3} B₂ = {1, t, t²} V₂ =R[t]<2 1 V3 = M2x2 (R) B3 = - - ( ) ( ) ( ) ( ) 0 1 Now consider the following two linear transformations: T (₁) T(b)=a+b-ct + at² C S(a + a₁ + a₂t²) = ao-a₂ a1 ao + a₁ a2 (a) Compute [T] (b) Compute [S] (c) Compute [ST] and verify that [ST]B³ = [S]B³₂[T]B³²

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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simple answers with explanations for three parts would do well. Thank you very much

4) Consider the following three vector spaces with corresponding basis: V₁ =R³ B₁ = {e₁,e2, e3} B₂ = {1, t, t²} V₂ =R[t]<2 1 V3 = M2x2 (R) B3 = - - ( ) ( ) ( ) ( ) 0 Now consider the following two linear transformations: T (1) T(b)=a+b-ct + at² C S(a + a₁ + a₂t²) = 00 - 02 01 ao + a₁ a2 (a) Compute [T]² B₁ (b) Compute [S]2 (c) Compute [ST] and verify that [ST]B³ = [S]B³₂[T]B³²
Transcribed Image Text:4) Consider the following three vector spaces with corresponding basis: V₁ =R³ B₁ = {e₁,e2, e3} B₂ = {1, t, t²} V₂ =R[t]<2 1 V3 = M2x2 (R) B3 = - - ( ) ( ) ( ) ( ) 0 Now consider the following two linear transformations: T (1) T(b)=a+b-ct + at² C S(a + a₁ + a₂t²) = 00 - 02 01 ao + a₁ a2 (a) Compute [T]² B₁ (b) Compute [S]2 (c) Compute [ST] and verify that [ST]B³ = [S]B³₂[T]B³²
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