Answer to Question #281096 in Linear Algebra for Himani

Question

Let U and W be subspaces of a vector space V of finite dimension. Prove that(UnW)°=U°+W°

Answer 1

To prove this, three things must be ascertained:

i. It must not be empty.

ii. The sum of the two sets must hold.

iii. The scalar multiplication of the two sets must hold.

i) 0=0+0, elements of U + W

ii) ß(U + W)= ẞU + ẞW, elements of U+W

iii) (U₁+W₁) + (U₂+W₂)= (U₁+U₂) +(W₁+W₂), elements of U+W

https://youtu.be/Rcj1-E3SAhs