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

Solutions for Chapter 5.2: More Work with Exponents and Scientific Notation

Intermediate Algebra | 6th Edition | ISBN: 9780321785046 | Authors: Elayn El Martin-Gay

Full solutions for Intermediate Algebra | 6th Edition

ISBN: 9780321785046

Intermediate Algebra | 6th Edition | ISBN: 9780321785046 | Authors: Elayn El Martin-Gay

Solutions for Chapter 5.2: More Work with Exponents and Scientific Notation

Solutions for Chapter 5.2
4 5 0 303 Reviews
22
5
Textbook: Intermediate Algebra
Edition: 6
Author: Elayn El Martin-Gay
ISBN: 9780321785046

This textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. Intermediate Algebra was written by and is associated to the ISBN: 9780321785046. Since 106 problems in chapter 5.2: More Work with Exponents and Scientific Notation have been answered, more than 62902 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.2: More Work with Exponents and Scientific Notation includes 106 full step-by-step solutions.

Key Math Terms and definitions covered in this textbook
  • Affine transformation

    Tv = Av + Vo = linear transformation plus shift.

  • Augmented matrix [A b].

    Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

  • Column picture of Ax = b.

    The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

  • Distributive Law

    A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

  • 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.

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

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

  • Free variable Xi.

    Column i has no pivot in elimination. We can give the n - r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

  • 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 .

  • Independent vectors VI, .. " vk.

    No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

  • 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.

  • Linear combination cv + d w or L C jV j.

    Vector addition and scalar multiplication.

  • Normal matrix.

    If N NT = NT N, then N has orthonormal (complex) eigenvectors.

  • Pascal matrix

    Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

  • 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.

  • Pivot columns of A.

    Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

  • Rank r (A)

    = number of pivots = dimension of column space = dimension of row space.

  • Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.

    Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

  • Semidefinite matrix A.

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

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

    Spectral radius = max of IAi I.

  • Wavelets Wjk(t).

    Stretch and shift the time axis to create Wjk(t) = woo(2j t - k).

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