7. Consider a subspace
1
0
6
U = span \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} = b_1, b_2 = \begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix} \subset \mathbb{R}^3 \text{and } x = \begin{bmatrix} 6 \\ 0 \\ 0 \end{bmatrix}
(a) Find the coordinates of \lambda of x in terms of the subspace U.
(b) Find the projection point \pi_U(x).
(c) Calculate the projection error.
(d) Find the projection matrix P_\pi
(e) Using Gram-Schmidt method, turn basis B = (b_1, b_2) of U \subset \mathbb{R}^3 into an ONB
C = (c_1, c_2) of U
