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Gokul posted an Question
November 18, 2020 • 14:05 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Vector space v properly contains subspaces w and t. dimensions of w and t are 3 and 5. what is the minimum possible dimension of v? a. 5 b. 6 c. 8 d. 15

Vector space V properly contains subspaces W and T. Dimensions of W and T are 3 and 5. What is the minimum possible dimension of V? A. 5 B. 6 C. 8 D. 15

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  • Srinath

    Since we are talking about minimum, we can take V to be the union of W and T. Either W and T have only {0} in common.... or they don't. In the first case, the dimension of V would simply be 8, by definition of direct product. If not, then the dimension of intersection of W and T would be 1 or 2 or 3... We can't choose 3, because it is given that V properly contains W and T.... therefore taking dimension of intersection of W and T to be 2, V has dimension 6, the required minimum.

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