Question 7.1.4: Find the coordinates of x = [ 1 2 3 4 ] with respect to the ...

Find the coordinates of \vec{x} = \begin{bmatrix}1\\2\\3\\4\end{bmatrix} with respect to the orthonormal basis

\mathcal{B} = \left\{ \frac{1}{2} \begin{bmatrix}1\\2\\3\\4\end{bmatrix}, \frac{1}{2} \begin{bmatrix}1\\2\\3\\4\end{bmatrix}, \frac{1}{\sqrt{2}} \begin{bmatrix}1\\2\\3\\4\end{bmatrix}, \frac{1}{\sqrt{2}} \begin{bmatrix}1\\2\\3\\4\end{bmatrix}\right\}