4. (i) Let v1 = 〈1, 2, 0, 3〉 , v2 = 〈4, 0, 5, 8〉, v3 = 〈8, 1, 5, 6〉 and W a subspace of R4 spanned by {v1, v2, v3}. Use the Gram- Schmidt process to find an orthogonal basis for W . (ii) Use the orthogonal basis found in Part (a) to find the best approximation to b = 〈1, 0, −4, 2〉 in the Span {v1, v2, v3}. (iii) Find the error vector of the approximation of Part (ii).

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