Consider vector space V over field F and linear mapping PE L(V) satisfying P2 := Po P = O, where o is a standard operation of composition and O is a zero mapping. Select all true statements. P(V) = {0} necessarily, where 0 denotes a zero vector from V. nul(P) < rk(P) P3.Ρo PoP =Θ. P(V) C ker P.

Consider vector space V over field F and linear mapping PE L(V) satisfying P2 := Po P = O, where o is a standard operation of composition and O is a zero mapping. Select all true statements. P(V) = {0} necessarily, where 0 denotes a zero vector from V. nul(P) < rk(P) P3.Ρo PoP =Θ. P(V) C ker P.

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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Consider vector space V over field F and linear mapping PE L(V) satisfying P² := P o P = O,
where o is a standard operation of composition and O is a zero mapping. Select all true statements.
P(V) = {0} necessarily, where 0 denotes a zero vector from V.
nul(P) < rk(P)
Р3 :— Ро РоР— Ө.
P(V) C ker P.

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