Consider the Euclidean vector space R3 with the dot product. A subspace U CR3 and vector x ? R3 are given by U = span {0 0 ,X= 0 (a) Show that x&U. (b) Determine the orthogonal projection au(x) of x onto U. Show that au(x) can be written as a linear combination of (1,1,1]T and (2,2, 3]. (c) Determine the distance d(x,U).

Consider the Euclidean vector Space 1&3 with the dot product. A subSpace U C 11113 and vector x 6 R3 are given by 1 2 1 U=span 1 , 2 ,x= 0 1 3 3 (a) Show that x 9! U. (h) Determine the orthogonal projection arU(x) of x onto U. Show that y (3:) can be written as a linear combination of [1, 1, 1]T and [2, 2, 3]T. (c) Determine the distance d.(x, U)