Show that {u1, uz} is an orthogonal basis for R2. Then express x as a linear combination ofthe us 3 8 d 2 u1= ,u2= ,an x= -4 6 -1 Which of the following criteria are necessary for a set of vectors to be an orthogonal basis for R2? Select all that apply. "l A. The vectors must all have a length of 1. fl B. The distance between any pair of distinct vectors must be constant. rd.' (3- The vectors must span R2. [if D. The vectors must form an orthogonal set. Which theorem could help prove one ofthese criteria from another? ' A- If S = {u1, up} is a basis in RP, then the members of S span RP and hence form an orthogonal set. . B. If S = {n.1, up} and the distance between any pair of distinct vectors is constant, then the vectors are evenly spaced and hence form an orthogonal set. . C. If S = {u1, up} and each ui has length 1, then S is an orthogonal set and hence is a basis for the subspace spanned by S. .V D. If S = {u1, up} 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. What calculation shows that {u1. uz} is an orthogonal basis for R2? Since the inner product of u1 and u2 is O , the vectors form an orthogonal set. From the theorem above, this proves that the vectors are also a basis for R2 because they are two linearly independent vectors in R2. Express x as a linear combination of the u's. x = u1 + u2 (Simplify your answers. Use integers or fractions for any numbers in the equation.)