\(\left\{ \begin{bmatrix} \frac{1}{\sqrt{2}}\\0\\-\frac{1}{\sqrt{2}}\end{bmatrix}, \begin{bmatrix} \frac{1}{\sqrt{2}}\\0\\\frac{1}{\sqrt{2}}\end{bmatrix}, \begin{bmatrix} 0\\-1\\0\end{bmatrix}\right\}\) is an orthonormal basis for \(\mathbb{R}^3\).
True
False