Question

Decide if each of the following statements is true or false. Justify your conclusion with an explanation or counter-example, as appropriate.

1. Applying Gram-Schmidt to an orthogonal set of vectors returns the vectors unchanged.
A. true
B. false

Answer 1

Applying Gram-Schmidt to an orthogonal set of vectors does not return the vectors unchanged. The statement is false. So the correct answer is Option A.

Step-by-step explanation:

The statement is false. When applying the Gram-Schmidt process to an orthogonal set of vectors, the resulting vectors will not be the same as the original vectors. The Gram-Schmidt process is used to orthogonalize a set of vectors, which means the resulting vectors will be orthogonal to each other but not necessarily the same as the original vectors.