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Business Math, 9th Edition - Solutions by Chapter

Business Math, | 9th Edition | ISBN: 9780135108178 | Authors: Cheryl Cleaves, Margie Hobbs, Jeffrey Noble

Full solutions for Business Math, | 9th Edition

ISBN: 9780135108178

Business Math, | 9th Edition | ISBN: 9780135108178 | Authors: Cheryl Cleaves, Margie Hobbs, Jeffrey Noble

Business Math, | 9th Edition - Solutions by Chapter

Solutions by Chapter
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Textbook: Business Math,
Edition: 9
Author: Cheryl Cleaves, Margie Hobbs, Jeffrey Noble
ISBN: 9780135108178

This textbook survival guide was created for the textbook: Business Math, , edition: 9. The full step-by-step solution to problem in Business Math, were answered by Patricia, our top Math solution expert on 03/08/18, 08:36PM. Business Math, was written by Patricia and is associated to the ISBN: 9780135108178. Since problems from 77 chapters in Business Math, have been answered, more than 4104 students have viewed full step-by-step answer. This expansive textbook survival guide covers the following chapters: 77.

Key Math Terms and definitions covered in this textbook
  • Cholesky factorization

    A = CTC = (L.J]))(L.J]))T for positive definite A.

  • Complex conjugate

    z = a - ib for any complex number z = a + ib. Then zz = Iz12.

  • Diagonalization

    A = S-1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k S-I.

  • Echelon matrix U.

    The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

  • Elimination matrix = Elementary matrix Eij.

    The identity matrix with an extra -eij in the i, j entry (i #- j). Then Eij A subtracts eij times row j of A from row i.

  • Elimination.

    A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

  • Factorization

    A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

  • Jordan form 1 = M- 1 AM.

    If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

  • lA-II = l/lAI and IATI = IAI.

    The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n - 1, volume of box = I det( A) I.

  • Left nullspace N (AT).

    Nullspace of AT = "left nullspace" of A because y T A = OT.

  • Lucas numbers

    Ln = 2,J, 3, 4, ... satisfy Ln = L n- l +Ln- 2 = A1 +A~, with AI, A2 = (1 ± -/5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

  • Nullspace N (A)

    = All solutions to Ax = O. Dimension n - r = (# columns) - rank.

  • Orthogonal subspaces.

    Every v in V is orthogonal to every w in W.

  • Permutation matrix P.

    There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or -1) based on the number of row exchanges to reach I.

  • Projection p = a(aTblaTa) onto the line through a.

    P = aaT laTa has rank l.

  • Solvable system Ax = b.

    The right side b is in the column space of A.

  • Spectrum of A = the set of eigenvalues {A I, ... , An}.

    Spectral radius = max of IAi I.

  • Subspace S of V.

    Any vector space inside V, including V and Z = {zero vector only}.

  • Toeplitz matrix.

    Constant down each diagonal = time-invariant (shift-invariant) filter.

  • Vector v in Rn.

    Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

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