Let-V-and-W-be-4-dimensional-subspaces-of-a-7-dimensional-vector-space-X-Which-of-the-following-CANNOT-be-the-dimension-of-the-subspace-V-W-A-0-B-1-C-2-D-3-E-4-

Tinku Tara June 3, 2023 Vector 0 Comments

Question Number 12752 by tawa last updated on 30/Apr/17

Let V and W be 4 dimensional subspaces of a 7 dimensional vector space X. Which of the following CANNOT be the dimension of the subspace V∩W. (A) 0 (B) 1 (C) 2 (D) 3 (E) 4

$$\mathrm{Let}\:\mathrm{V}\:\mathrm{and}\:\mathrm{W}\:\mathrm{be}\:\mathrm{4}\:\mathrm{dimensional}\:\mathrm{subspaces}\:\mathrm{of}\:\mathrm{a}\:\mathrm{7}\:\mathrm{dimensional}\:\mathrm{vector}\:\mathrm{space}\:\mathrm{X}. \\ $$$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{CANNOT}\:\mathrm{be}\:\mathrm{the}\:\mathrm{dimension}\:\mathrm{of}\:\mathrm{the}\:\mathrm{subspace}\:\mathrm{V}\cap\mathrm{W}. \\ $$$$\left(\mathrm{A}\right)\:\mathrm{0}\:\left(\mathrm{B}\right)\:\mathrm{1}\:\left(\mathrm{C}\right)\:\mathrm{2}\:\left(\mathrm{D}\right)\:\mathrm{3}\:\left(\mathrm{E}\right)\:\mathrm{4} \\ $$

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Let-V-and-W-be-4-dimensional-subspaces-of-a-7-dimensional-vector-space-X-Which-of-the-following-CANNOT-be-the-dimension-of-the-subspace-V-W-A-0-B-1-C-2-D-3-E-4-

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