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1 1 0 3 1 0 1 4 4. (OC19) Let u; = o =g w= 10 and y = i Let W = Span{u;, ug, us}. -1 1 1 6 (a) Verfiy that {u;, us,us} forms an orthogonal set. (b) Find the projection of y onto W. (c) Let x = . Find the projection of x onto W. How would you interpret your answer? O = = b 5. (OC20) Let @ be a matrix with orthonormal columns, and let T'(x) = @x be the transformation defined by (). Explain why T is angle-preserving. That is, explain why the angle between u and v in the domain will be the same as the angle between 7'(u) and T'(v) in the codomain. (Hint: Remember that we can use the dot product to help us find the angle between two vectors!) 6. (0C20) Suppose that U and V both have orthonormal columns and that UV is defined. (a) Show that UV has orthonormal columns. (b) If U and V are n X n orthogonal matrices, show that UV is an orthogonal matrix