Question

Let R4 have the inner product <u, v>  =  u1v1 + 2u2v2 + 3u3v3 + 4u4v4...

Let R4 have the inner product

<u, v>  =  u1v1 + 2u2v2 + 3u3v3 + 4u4v4

(a) Let w  =  (0, 6, 4, 1). Find ||w||.
(b) Let W be the subspace spanned by the vectors

u1  =  (0, 0, 2, 1), and   u2  =  (3, 0, −2, 1).

Use the Gram-Schmidt process to transform the basis {u1, u2} into an orthonormal basis {v1, v2}. Enter the components of the vector v2 into the answer box below, separated with commas.

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