Define linear transformations S: P, → P2 and T: P2 P¸ by S(a + bx) = a + (a + b)x + 4bx? and T(a + bx + cx?) = b + 4cx. Compute (S o T)(5 + 4x – x²) and (S o T((a + bx + cx?). (So T)(5 + 4x – x²) = (S o T)(a + bx + cx²) = Can you compute (T o S)(a + bx)? If so, compute it. (If an answer does not exist, enter DNE.) (To S)(a + bx) =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Define linear transformations S : P, → P, and T: P, - P, by
S(a + bx) = a + (a + b)x + 4bx2
and
T(a + bx + cx2) = b + 4cx.
Compute (S o T)(5 + 4x – x2) and (S o T)(a + bx + cx2).
(SO T)(5 + 4x – x2) =
(SO T)(a + bx + cx?) =
Can you compute (To S)(a + bx)? If so, compute it. (If an answer does not exist, enter DNE.)
(To S)(a + bx) =
Transcribed Image Text:Define linear transformations S : P, → P, and T: P, - P, by S(a + bx) = a + (a + b)x + 4bx2 and T(a + bx + cx2) = b + 4cx. Compute (S o T)(5 + 4x – x2) and (S o T)(a + bx + cx2). (SO T)(5 + 4x – x2) = (SO T)(a + bx + cx?) = Can you compute (To S)(a + bx)? If so, compute it. (If an answer does not exist, enter DNE.) (To S)(a + bx) =
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