5. 3) Let : R₂[x] →→ R³ be a linear transformation such that (6) (a) Find a formula for l(a + bx + cx²). (b) Show that is a vector space isomorphism and find a formula for l-¹. (1) = = l(x): = 0 and l(x²) = = 1

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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5.
3) Let : R₂[x] → R³ be a linear transformation such that
(
(1) =
=
l(x):
=
0
and
l(x²) =
=
1
(a) Find a formula for l(a + bx + cx²).
(b) Show that is a vector space isomorphism and find a formula for l-¹.
Transcribed Image Text:5. 3) Let : R₂[x] → R³ be a linear transformation such that ( (1) = = l(x): = 0 and l(x²) = = 1 (a) Find a formula for l(a + bx + cx²). (b) Show that is a vector space isomorphism and find a formula for l-¹.
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