T:R2[r] → R³ is given by ao + 2a1 + az T(ao +a1x + a2x²) = ( 3a0 + 5a1 + 5az ( 2ao + 3a1 + 4a2) a) Write down the matrix of T with respect to (1,x, r²) and (eỉ, ,). b) Determine if T is an isomorphism.

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...
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T:R2[r] → R³ is given by
ao + 2a1 + az
T(ao +a1x + a2x²) = ( 3a0 + 5a1 + 5az
( 2ao + 3a1 + 4a2)
a)
Write down the matrix of T with respect to (1,z, r²) and (eỉ, , e).
b)
Determine if T is an isomorphism.
Transcribed Image Text:T:R2[r] → R³ is given by ao + 2a1 + az T(ao +a1x + a2x²) = ( 3a0 + 5a1 + 5az ( 2ao + 3a1 + 4a2) a) Write down the matrix of T with respect to (1,z, r²) and (eỉ, , e). b) Determine if T is an isomorphism.
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