Let V be an inner product space and let v1, v2, v3 ∈ V be an orthogonal set of vectors. Which of the following statements is true?
1
The vectors 5v1 + 6v2 + 7v3, 5v2 + v3, v2 + 3v3 can be extended to a basis of V.
2
The vectors 4v1 + v2 + 2v3, v2 + 3v3, v2 + 3v3 can be extended to an orthogonal basis of V.
3
The vectors v1 + v2 + 2v3, v2 + v3, 2v1 + v2 + 3v3 can be extended to a basis of V.
4
The vectors 2v1 + v2 + 2v3, 2v1 + v2 + v3, 2v1 + v2 + 3v3 can be extended to a basis of V.