Mathematics · Linear Algebra
Let V be an inner product space and let v1, v2, v3 ∈ V be a non-zero orthogonal set of vectors. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The vectors v1 + v2 + 2v3, 2v1 + v2 + v3, 2v1 + v2 + 3v3 can be extended to a basis of V.
- 2The vectors v1 + v2 + 2v3, v2 + v3, 2v1 + v2 + 3v3 can be extended to a basis of V.
- 3The vectors v1 + v2 + 2v3, v2 + v3, v2 + 3v3 can be extended to an orthogonal basis of V.
- 4The vectors v1 + v2 + 2v3, v2 + v3, v2 + 3v3 can be extended to a basis of V.✓
Correct answer
The vectors v1 + v2 + 2v3, v2 + v3, v2 + 3v3 can be extended to a basis of V.
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