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