Let fi =1+2r - 2x², f2 = 2+3x – 4x², f3 = 1+4x – x² and setB = (f1; f2, f3). T :R2[x] → M2×2(R) is a linear transformation which satisfiesT(fi) = (; 5).T)„T') = (; :).T(s) =5 10,3Determine T(1), T(r), and T(x²) and then a formula for T(ao +a1x+azx²).

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Let fi =1+2r– 2r², f2 = 2+3r – 4r², f3 = 1+4x – r² and set B = (f1, f2, f3). T:R2[r] → M2×2(R) is a linear transformation which satisfies T(S) = (; :) .Ts) = (; ) . T5) = (; %)- Determine T(1), T(z), and T(r²) and then a formula for T(ao + a,x+azx²).

Let fi =1+2r– 2r², f2 = 2+3r – 4r², f3 = 1+4x – r² and set B = (f1, f2, f3). T:R2[r] → M2×2(R) is a linear transformation which satisfies T(S) = (; :) .Ts) = (; ) . T5) = (; %)- Determine T(1), T(z), and T(r²) and then a formula for T(ao + a,x+azx²).

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 4CM

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Question

Let fi =1+2r - 2x², f2 = 2+3x – 4x², f3 = 1+4x – x² and set
B = (f1; f2, f3). T :R2[x] → M2×2(R) is a linear transformation which satisfies
T(fi) = (; 5).T)
„T') = (; :).T(s) =
5 10,
3
Determine T(1), T(r), and T(x²) and then a formula for T(ao +a1x+azx²).

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