If {v₁, v₂, v₃} is an orthogonal basis for W, then multiplying v₃ by a scalar c gives a new orthogonal basis {v₁, v₂, v₃}.
A. False. If the scale factor is zero it will not give a new orthogonal basis
B. False. If the scale factor is negative it will not give a new orthogonal basis °
C. True. For example, when the vectors in an orthogonal set are normalized, they are multiplied by scalars, and the set of new vectors is orthogonal 0
D. True. Multiplication by a scalar c will change the length of v₃ but it will not change the relative angles between the vectors and so they will still be orthogonal