Consider vector space V over field F. Consider set of all linear mappings from vector space V to vector space V, i.e. set L(V). Linear mappings from L(V) can be naturally added and multiplied by a scalar from F. Select all true statements. Set L(V) with given operations is a vector space. V = ker A U A(V) for every linear mapping A from L(V), because dim V = nul(A) + rk(A). Multiplication of linear mapping from L(V) by a scalar from F is again a linear mapping from L(V). Composition of two linear mappings from L(V) is again a linear mapping from L(V).

Consider vector space V over field F. Consider set of all linear mappings from vector space V to vector space V, i.e. set L(V). Linear mappings from L(V) can be naturally added and multiplied by a scalar from F. Select all true statements. Set L(V) with given operations is a vector space. V = ker A U A(V) for every linear mapping A from L(V), because dim V = nul(A) + rk(A). Multiplication of linear mapping from L(V) by a scalar from F is again a linear mapping from L(V). Composition of two linear mappings from L(V) is again a linear mapping from L(V).

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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