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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).

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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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).
Transcribed Image Text: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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