×
Log in to StudySoup
Get Full Access to Math - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Math - Textbook Survival Guide

Solutions for Chapter 8-2: LOGARITHMIC FORM OF AN EXPONENTIAL EQUATION

Amsco's Algebra 2 and Trigonometry | 1st Edition | ISBN: 9781567657029 | Authors: Gantert

Full solutions for Amsco's Algebra 2 and Trigonometry | 1st Edition

ISBN: 9781567657029

Amsco's Algebra 2 and Trigonometry | 1st Edition | ISBN: 9781567657029 | Authors: Gantert

Solutions for Chapter 8-2: LOGARITHMIC FORM OF AN EXPONENTIAL EQUATION

Solutions for Chapter 8-2
4 5 0 246 Reviews
18
1
Textbook: Amsco's Algebra 2 and Trigonometry
Edition: 1
Author: Gantert
ISBN: 9781567657029

This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. Chapter 8-2: LOGARITHMIC FORM OF AN EXPONENTIAL EQUATION includes 77 full step-by-step solutions. Since 77 problems in chapter 8-2: LOGARITHMIC FORM OF AN EXPONENTIAL EQUATION have been answered, more than 30953 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029.

Key Math Terms and definitions covered in this textbook
  • Associative Law (AB)C = A(BC).

    Parentheses can be removed to leave ABC.

  • Cyclic shift

    S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

  • 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.

  • Exponential eAt = I + At + (At)2 12! + ...

    has derivative AeAt; eAt u(O) solves u' = Au.

  • Fourier matrix F.

    Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

  • Gauss-Jordan method.

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

  • Graph G.

    Set of n nodes connected pairwise by m edges. A complete graph has all n(n - 1)/2 edges between nodes. A tree has only n - 1 edges and no closed loops.

  • Krylov subspace Kj(A, b).

    The subspace spanned by b, Ab, ... , Aj-Ib. Numerical methods approximate A -I b by x j with residual b - Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

  • Left nullspace N (AT).

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

  • Network.

    A directed graph that has constants Cl, ... , Cm associated with the edges.

  • Orthogonal subspaces.

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

  • Random matrix rand(n) or randn(n).

    MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

  • Semidefinite matrix A.

    (Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

  • Singular matrix A.

    A square matrix that has no inverse: det(A) = o.

  • Special solutions to As = O.

    One free variable is Si = 1, other free variables = o.

  • Standard basis for Rn.

    Columns of n by n identity matrix (written i ,j ,k in R3).

  • Subspace S of V.

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

  • Triangle inequality II u + v II < II u II + II v II.

    For matrix norms II A + B II < II A II + II B IIĀ·

  • Vector addition.

    v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

  • Vector v in Rn.

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

×
Log in to StudySoup
Get Full Access to Math - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Math - Textbook Survival Guide
×
Reset your password