Let V be a vector space with finite dimensional. Let subset S of V be:
. . . . .\(\displaystyle .S^0\, =\, \left\{\,f\, \in\, V^{*}\, \bigl|\bigr.\,\right.\) \(\displaystyle f(u)\, =\, 0\,\) \(\displaystyle \left. \forall\, u\, \in\, S\,\right\}\)
Prove that if W1 and W2 are subspaces of V then:
. . . . .\(\displaystyle \left(W_1\, \cap\, W_2\right)^0\, =\, W_1^0\, +\, W_2^0\)
I succeed in proving that the right side is contained in the left side of the equation, but I didn't succeed to prove the opposite direction.
I think I should do here something with bases for each of the spaces here, but I don't know how.
Please help me here...
. . . . .\(\displaystyle .S^0\, =\, \left\{\,f\, \in\, V^{*}\, \bigl|\bigr.\,\right.\) \(\displaystyle f(u)\, =\, 0\,\) \(\displaystyle \left. \forall\, u\, \in\, S\,\right\}\)
Prove that if W1 and W2 are subspaces of V then:
. . . . .\(\displaystyle \left(W_1\, \cap\, W_2\right)^0\, =\, W_1^0\, +\, W_2^0\)
I succeed in proving that the right side is contained in the left side of the equation, but I didn't succeed to prove the opposite direction.
I think I should do here something with bases for each of the spaces here, but I don't know how.
Please help me here...
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