:: Answers to practise problems for best approximation

    1. \( \operatorname{proj}_U \mathbf{v} = (15/7, -16/7, -18/7) \)
    2. \( d = 10 \, \sqrt{2 / 7} \)
    1. \( \operatorname{proj}_U \mathbf{v} = (22/31, 0, 77/31, 33/31) \)
    2. \( d = 2 \sqrt{17/31} \)
    1. \( \operatorname{proj}_U \mathbf{v} = \begin{bmatrix} 0 \\ & 1 \\ & & 0 \end{bmatrix} \)
    2. \( d = \sqrt{2} \)
    1. \( \operatorname{proj}_U \mathbf{v} = (-9940 e + 27020) x^3 + (15120 e - 41100) x^2 + (-6180 e + 16800) x + 536 e - 1456 \)
    2. \(\displaystyle d = \sqrt{\frac{(1001 e - 2721) (193 - 71 e)}{2}} \)
    1. \( \operatorname{proj}_U \mathbf{v} = \frac{1}{15} \, (4 + 21 \mathrm{i}, 6 + 6 \mathrm{i}, 1 + 25 \mathrm{i}) \)
    2. \( d = \sqrt{13/15} \)
    1. \( \operatorname{proj}_U \mathbf{v} = \begin{bmatrix} 0 \\ & 1 \\ & & 0 \end{bmatrix} \)
    2. \( d = 2 \)