Let U and V denote vector spaces over F. Consider o: U →→ V denote a linear transformation where nullity(o) = m and dim(U) = n with n > m. Show that {o(vm+1), O(Vm+2), ..., σ(v₁)} forms a basis for Im(o).
Let U and V denote vector spaces over F. Consider o: U →→ V denote a linear transformation where nullity(o) = m and dim(U) = n with n > m. Show that {o(vm+1), O(Vm+2), ..., σ(v₁)} forms a basis for Im(o).
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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Transcribed Image Text:Let U and V denote vector spaces over F.
Consider o: U →→ V denote a linear transformation where nullity(o) = m and dim(U) = n
with n > m.
Show that {o (vm+1), O(Vm+2), ..., o(vn)} forms a basis for Im(o).
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