(Solved): Determine whether the set of vectors is orthonormal. If the set is only orthogonal, normalize the v ...

Determine whether the set of vectors is orthonormal. If the set is only orthogonal, normalize the vectors to produce an orthonormal set. ${\mathbf{u}}_1=\left[\begin{array}{c}\frac{1}{\sqrt{145}}\\ \frac{12}{\sqrt{290}}\\ \frac{12}{\sqrt{290}}\end{array}\right],{\mathbf{u}}_2=\left[\begin{array}{c}12\\ -\frac{1}{\sqrt{290}}\\ -\frac{1}{\sqrt{290}}\end{array}\right],{\mathbf{u}}_3=\left[\begin{array}{c}0\\ \frac{1}{\sqrt{2}}\\ -\frac{1}{\sqrt{2}}\end{array}\right]$ Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The set of vectors is orthogonal only. The normalized vectors for ${\mathbf{u}}_1,{\mathbf{u}}_2$ and ${\mathbf{u}}_3$ are and , respectively. B. The set of vectors is orthonormal. C. The set of vectors is not orthogonal.