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1. Let u1 = HN U2 U3 = -2 U4 = Show that {U1, U2, U3, U4} is an N orthogonal basis for 4. 2. Let U1, U2, U3, U4 be given as in problem 1, and let v = Write v as a sum of two - A vectors, with one in span{uj, u2} and the other in span{u3, u4}. 3. Let U1, U2, U3, U4 be given as in problem 1. Find the orthogonal projection of v = onto span{u1, U2, U3}. 4. Let U1, U2, Ug, u4 be given as in problem 1. Find the distance from v = to span {u1, U2, U3}. 5. Let us - ( ? ).= - (2)a.. and U3 = - 2 Write v = as a sum of vectors in W = span{u1, u2, U3} and WI. NWA 6. Find the best approximation of v = by a vector of the form a + b 7. Mark each of the following as true or false. Justify your answers. a. If W is a subspace of R" and y is a vector in both W and WA, then y is the zero vector. b. Suppose W is a subspace of " . If v E R" can be written as v = Z1 + Z2 where z, E W and Z2 E W, then z1 = projwv and Z2 = projwiv. . Suppose W is a subspace of ". The best approximation of a vector v E R" by a vector in W- has the form v - projwv . d. If an n x p real matrix U has orthonormal columns, then UUT x = x for all x E R"