images of the standard basis vectors with respect to the given linear transformation. 15. fi = 1+2x – 2x2, f2 = 2+ 3x – 4x2, f3 = 1 + 4.x – x², B = (f1, f2, f3). 1 ‚T(f2) = 2, 1 4 T(fi) = s),T(f3) = (; 3 5 5 8 5 10

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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a) Verify the given sequence B is a basis ; and b) compute the
images of the standard basis vectors with respect to the given linear transformation.
15. fi = 1+2x – 2x2, f2 = 2 + 3x – 4x2, f3 = 1 + 4x – x², B = (f1, f2, f3).
-
1
T(fi) = (; 10)-
4
T(fi) = (; ).T
,T(f2) :
3
8
Transcribed Image Text:a) Verify the given sequence B is a basis ; and b) compute the images of the standard basis vectors with respect to the given linear transformation. 15. fi = 1+2x – 2x2, f2 = 2 + 3x – 4x2, f3 = 1 + 4x – x², B = (f1, f2, f3). - 1 T(fi) = (; 10)- 4 T(fi) = (; ).T ,T(f2) : 3 8
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