Help needed on the last part only 5 Show that {u,, u2, uz is an orthogonal basis for R. Then express x as a linear combination of the u's.- 2and x =-21= En6.u, =u2 =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.YA. The vectors must form an orthogonal set.B. The vectors must all have a length of 1.OC. The distance between any pair of distinct vectors must be constant.D. The vectors must span W.Which theorem could help prove one of these criteria from another?O A. 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 setOB. If S= {uu, and each u, has length 1, then S is an orthogonal set and hence is a basis for the subspace spanned by S.OC. IfS= {u·u) is a basis in RP, then the members of S span RP and hence form an orthogonal set.D. 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.Which calculations should be performed next?(Simplify your answers.)O A. u,u1 =u1 u2 =U2 U2 == En. 'n0.= En. EnHow do these calculations show that (u,, u,, u is an orthogonal basis for R?Since each inner product isthe vectors form an orthogonal set. From the theorem above, this proves that the vectors are also a basis.Express x as a linear combination of the u's.u, +U2 +U3(Use integers or fractions for any numbers in the equation.)

Name: Help needed on the last part only 5 Show that {u,, u2, uz is an orthog
Uploaded: 2024-03-05T11:52:21.000Z
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Description: Help needed on the last part only 5 Show that {u,, u2, uz is an orthogonal basis for R. Then express x as a linear combination of the u's.- 2and x =-21= En6.u, =u2 =Which of the following criteria are necessary for a set of vectors to be an orthogona