Notation: In the following questions, underlined letters such as g, b, etc. denote column vectors
of proper length; boldface letters such as A, B, etc. denote matrices of proper size; means
the transpose of matrix A. is the (n x n) identity matrix. ||αl| means the Euclidean norm of
vector @. R is the usual set of all real nun det
(A) is the determinant of square matrix A.
row
(A) and col
(A) are the row and column spaces of A over R, respectively. For any linear map
T over vector spaces, we use ker(T), rank(T') and nullity(T) for the kernel, rank and nullity of
T, respectively. Let W be a subspace of , then by W ┴ we mean the orthogonal complement
of W in the Euclidean inner product space denote
the unilateral Laplace and inverse Laplace transforms for t 2 0, respectively.
八、 Consider a 3 x 3 nonzero matrix A, and let W = . The least
squares solutions xLs to Ax = b are illustrated in the following figure,where projwe b is the
orthogonal projection of vector b onto vector space W. A minimun length least squares
, solution EMurs is the one among the least squares solutions that has a minimum norm.
Which of the following stateme ents is/are true?
(A)
(B)
(C)
(D) The minimum length least squares solution EMLLS to Ax = b is unique, and =
projvxLs, where V = .
(E) None of the above are true.