6. Find the distance from the vector (1, 0, 0, 1) to the subspace of R4 defined by the equation 1 + 2 + 23 + 24 = 0. Answer: The standard way of finding a basis in this subspace gives columns of the matrix A = 1 0 O Then 2 1 1 AT A = 1 2 1 and Ab = 1 2 It is not a good idea to compute A(A4)-'A for a 3 x 3 matrix on the exam! Instead one just solves Ar = b by elimination, and easily obtains r = (-1/2, -1/2, 1/2), this is the "least square solution" of Ar = b. Then the projection is (1/2, -1/2, -1/2, 1/2), the difference is (1/2, 1/2, 1/2, 1/2) and the distance is 1