Suppose that we have linear transformations T:R" R" with the convention vT = w(where veR" and weR") and S:R"→R' with the convention wS = u(where weR" and u eR'). Given the fact that ToS:R" →R' exists, prove: (a) if T and S are one to one, then T o S is one-to-one. (b) if T and S are onto, then T-S is onto.

Suppose that we have linear transformations T:R" R" with the convention vT = w(where veR" and weR") and S:R"→R' with the convention wS = u(where weR" and u eR'). Given the fact that ToS:R" →R' exists, prove: (a) if T and S are one to one, then T o S is one-to-one. (b) if T and S are onto, then T-S is onto.

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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