Question

(a)
a
सदिश समष्टियों हेतु विस्तार का प्रमेय लिखिए एवं सिद्ध कीजिए।
State and prove Extension theorem for linear spaces.​

Answer 1

Extension Theorem. Every linearly independent list in a finite-dimensional vector space V can be extended to a basis. Idea: The idea of the proof is to suppose that (u1,..., um) is a linearly indepen- dent list in V . Since V is finite-dimensional, we can write V = span(w1,..., wn).