Mathematics · Linear Algebra
Let W1 = {[a, -b; b, 2a] : a, b ∈ &mathbb{R}} and W2 = {[a, -b; b, -a] : a, b ∈ &mathbb{R}} be two subspaces of the vector space M2(&mathbb{R}). Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1W1 + W2 is a proper subset of M2(&mathbb{R})
- 2W1 + W2 = M2(&mathbb{R})
- 3{[0, 0; 0, 0]} is a proper subset of W1 ∩ W2
- 4W1 ∩ W2 = {[0, 0; 0, 0]}✓
Correct answer
W1 ∩ W2 = {[0, 0; 0, 0]}
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