19. Let F be the set of polynomials in P(IR) that are divisible by x2 - 9 and Gthe set of polynomials in Pa(R) that are divisible by x – 27. Prove that F andG are subspaces of P4(R) and find their dimensions. Also find dim(FnG) anddim(F+ G).

Subspace: A non-empty subset of a vector space over is subspace if it satisfies following…

19. Let F be the set of polynomials in P(R) that are divisible by a2 - 9 and G the set of polynomials in Pa(R) that are divisible by r – 27. Prove that F and G are subspaces of Pa(R) and find their dimensions. Also find dim(FnG) and dim(F+ G).

19. Let F be the set of polynomials in P(R) that are divisible by a2 - 9 and G the set of polynomials in Pa(R) that are divisible by r – 27. Prove that F and G are subspaces of Pa(R) and find their dimensions. Also find dim(FnG) and dim(F+ G).

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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19. Let F be the set of polynomials in P(IR) that are divisible by x2 - 9 and G
the set of polynomials in Pa(R) that are divisible by x – 27. Prove that F and
G are subspaces of P4(R) and find their dimensions. Also find dim(FnG) and
dim(F+ G).

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