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- Show that {u,, u2, uz) is an orthogonal basis for R. Then express x as a linear combination of the u's. 3 2 1 4 u1 = - 3 u, = 2 u3 = and x= - 3 - 1 4 1 Which of the following criteria are necessary for a set of vectors to be an orthogonal basis for a subspace W of R"? Select all that apply. O A. The vectors must all have a length of 1. O B. The vectors must span W. O c. The vectors must form an orthogonal set. O D. The distance between any pair of distinct vectors must be constant. Which theorem could help prove one of these criteria from another? O A. If S= {u,, ., u, is an orthogonal set of nonzero vectors in R", then S is linearly independent and hence is a basis for the subspace spanned by S. O B. If S = {u,, ., u, and each u; has length 1, then S is an orthogonal set and hence is a basis for the subspace spanned by S. Oc. If S= {u, ., u,} and the distance between any pair of distinct vectors is constant, then the vectors are evenly spaced and hence form an orthogonal set. O D. If…If A and B are orthogonal, is A+B also orthogonal? Can you demonstrate Algebraically using A + B = (A + B)^T etc...? Thank you.Calculate û x ô if û = } + 2k and û = -i - ĵ + k.