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a 1.F.5 To any vector v = in R³ we can associate a polynomial p.(x) = ax² + bx + c in P<2. There is a linear transformation R3 → R³ where Pv(3) L(v) = | P.(3) P"(3) For example, when v = | 1| we have 5 Рo (г) — 2? + и + 5, р.(3) — 17, p.(2) — 2л + 1, p.(3) — 7, р"(ӕ) %3D 2, р"(3) — 2 and thus 17 L(v) = 7 %3D 2 Write down a matrix A such that L(v) = A · v. %3D

a 1.F.5 To any vector v = in R³ we can associate a polynomial p.(x) = ax² + bx + c in P<2. There is a linear transformation R3 → R³ where Pv(3) L(v) = | P.(3) P"(3) For example, when v = | 1| we have 5 Рo (г) — 2? + и + 5, р.(3) — 17, p.(2) — 2л + 1, p.(3) — 7, р"(ӕ) %3D 2, р"(3) — 2 and thus 17 L(v) = 7 %3D 2 Write down a matrix A such that L(v) = A · v. %3D

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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1.F.5 To any vector v = in R° we can associate a polynomial p„ (x) = ax² + bx + c in P<2. There is a linear transformation R3 → R³ where Pv(3) L(v) =| P.(3) P"(3) For example, when v = we have Рo (г) — 2? + а + 5, р.(3) — 17, pl(2) %— 2л + 1, p.(3) — 7, р"(ӕ) %3D 2, р"(3) — 2 and thus 17 L(v) = 7 Write down a matrix A such that L(v) = A · v.
Transcribed Image Text:1.F.5 To any vector v = in R° we can associate a polynomial p„ (x) = ax² + bx + c in P<2. There is a linear transformation R3 → R³ where Pv(3) L(v) =| P.(3) P"(3) For example, when v = we have Рo (г) — 2? + а + 5, р.(3) — 17, pl(2) %— 2л + 1, p.(3) — 7, р"(ӕ) %3D 2, р"(3) — 2 and thus 17 L(v) = 7 Write down a matrix A such that L(v) = A · v.
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