> > Business Math, 9

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
4 5 0 361 Reviews
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 8039 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
  • Change of basis matrix M.

    The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

  • Cofactor Cij.

    Remove row i and column j; multiply the determinant by (-I)i + j •

  • Column space C (A) =

    space of all combinations of the columns of A.

  • Complex conjugate

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

  • Fibonacci numbers

    0,1,1,2,3,5, ... satisfy Fn = Fn-l + Fn- 2 = (A7 -A~)I()q -A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

  • Full row rank r = m.

    Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

  • Gauss-Jordan method.

    Invert A by row operations on [A I] to reach [I A-I].

  • Hankel matrix H.

    Constant along each antidiagonal; hij depends on i + j.

  • Incidence matrix of a directed graph.

    The m by n edge-node incidence matrix has a row for each edge (node i to node j), with entries -1 and 1 in columns i and j .

  • Multiplication Ax

    = Xl (column 1) + ... + xn(column n) = combination of columns.

  • Nullspace N (A)

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

  • Particular solution x p.

    Any solution to Ax = b; often x p has free variables = o.

  • Projection matrix P onto subspace S.

    Projection p = P b is the closest point to b in S, error e = b - Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) -1 AT.

  • 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.

  • Symmetric matrix A.

    The transpose is AT = A, and aU = a ji. A-I is also symmetric.

  • Trace of A

    = sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

  • Unitary matrix UH = U T = U-I.

    Orthonormal columns (complex analog of Q).

  • Vector space V.

    Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

  • Volume of box.

    The rows (or the columns) of A generate a box with volume I det(A) I.

×
Log in to StudySoup
Get Full Access to Thousands of Study Materials at Your School

Forgot password? Reset password here

Join StudySoup for FREE
Get Full Access to Thousands of Study Materials at Your School
Join with Email
Already have an account? Login here
Reset your password

I don't want to reset my password

Need help? Contact support

Need an Account? Is not associated with an account
Sign up
We're here to help

Having trouble accessing your account? Let us help you, contact support at +1(510) 944-1054 or support@studysoup.com

Got it, thanks!
Password Reset Request Sent An email has been sent to the email address associated to your account. Follow the link in the email to reset your password. If you're having trouble finding our email please check your spam folder
Got it, thanks!
Already have an Account? Is already in use
Log in
Incorrect Password The password used to log in with this account is incorrect
Try Again

Forgot password? Reset it here