Prove Theorem 6.2: Let S={u_1, u_2, …, u_n} be a basis for V over K, and le…

Prove Theorem 6.2: Let S={u_1, u_2, …, u_n} be a basis for V over K, and let 𝐌 be the algebra of n square matrices over K. Then the mapping m: A(V) →𝐌 defined by m(T)=[T]_S is a vector space isomorphism. That is, for any F, G ∈A(V) and any k ∈K, we have (i) [F+G]=[F]+[G] (ii) [k F]=k[F] (iii) m is one-to-one and onto.

Watch the full video at:
https://www.numerade.com/ask/question/prove-theorem-62-let-sleftu_1-u_2-ldots-u_nright-be-a-basis-for-v-over-k-and-let-mathbfm-be-the-al-2-86308/?utm_medium=social&utm_source=youtube&utm_campaign=low_count_category

Never get lost on homework again. Numerade is a STEM learning website and app with the world’s largest STEM video library.
Join today and access millions of expert-created videos, each one skillfully crafted to teach you how to solve tough problems step-by-step.

Join Numerade today at:
https://www.numerade.com/signup/?utm_medium=social&utm_source=youtube&utm_campaign=low_count_category

Видео Prove Theorem 6.2: Let S={u_1, u_2, …, u_n} be a basis for V over K, and le… канала Thomas Carlson