Let
\mathbf{v}_1 = \left[\begin{array}{c}1\\2\\0\\-3\\0\\3\\\end{array}\right], \mathbf{v}_2 = \left[\begin{array}{c}0\\0\\5\\-3\\0\\2\\\end{array}\right], \text{ and } \mathbf{v}_3 = \left[\begin{array}{c}1\\0\\0\\-1\\3\\2\\\end{array}\right].
Use the Gram-Schmidt procedure to produce an orthogonal set with the same span. (Hint: If you have unlimited submissions, it might be useful to submit to check your answer for each vector \mathbf{u}_j before continuing.) Note: The \mathbf{u}_j must be given in the same order as provided by the standard procedure.

You can earn partial credit on this problem.