Question

Question: Let F,K and Kbe fields such that $\mathit{F}\mathbf{\subseteq }\mathit{K}\mathbf{\subseteq }\mathit{L}$. If $\mathit{S}\mathbf{=}\left\{v_1,v_2,v_{3,-------}{v}_n\right\}$spans Lover F, explain why Salso spans Lover K.

Short answer

Answer

Yes, we can say S spans L over K also.

Step-by-step solution

Explanation

Let$S=\left\{v_1,v_2,v_{3,-------}{v}_n\right\}$ spans L over F.

Every element of the vector spans can be obtained as a linear combination of the elements and those scalars belong to F.

Since.$F\subseteq K\subseteq L$

Every element of F is in K also.

Solution

$\therefore$those scalars which generated all element of belongs to K also .

$\therefore$we can say S spans L over K also.