 Chapter 1: Real Numbers and Algebraic Expressions
 Chapter 1.1: Tips for Success in Mathematics
 Chapter 1.2: Algebraic Expressions and Sets of Numbers
 Chapter 1.3: Operations on Real Numbers and Order of Operations
 Chapter 1.4: Properties of Real Numbers and Algebraic Expressions
 Chapter 10: Conic Sections
 Chapter 10.1: The Parabola and the Circle
 Chapter 10.2: The Ellipse and the Hyperbola
 Chapter 10.3: Solving Nonlinear Systems of Equations
 Chapter 10.4: Nonlinear Inequalities and Systems of Inequalities
 Chapter 11: Sequences, Series, and the Binomial Theorem
 Chapter 11.1: Sequences
 Chapter 11.2: Arithmetic and Geometric Sequences
 Chapter 11.3: Series
 Chapter 11.4: Partial Sums of Arithmetic and Geometric Sequences
 Chapter 11.5: The Binomial Theorem
 Chapter 2: EQUATIONS, INEQUALITIES, AND PROBLEM SOLVING
 Chapter 2.1: Linear Equations in One Variable
 Chapter 2.1  2.4: Linear Inequalities and Problem Solving
 Chapter 2.2: An Introduction to Problem Solving
 Chapter 2.3: Formulas and Problem Solving
 Chapter 2.4: Linear Inequalities and Problem Solving
 Chapter 2.5: Compound Inequalities
 Chapter 2.6: Absolute Value Equations
 Chapter 2.7: Absolute Value Inequalities
 Chapter 3: GRAPHS AND FUNCTIONS
 Chapter 3.1: Graphing Equations
 Chapter 3.13.5: Linear Equations in Two Variables
 Chapter 3.2: Introduction to Functions
 Chapter 3.3: Graphing Linear Functions
 Chapter 3.4: The Slope of a Line
 Chapter 3.5: Equations of Lines
 Chapter 3.6: Graphing PiecewiseDefined Functions and Shifting and Reflecting Graphs of Functions
 Chapter 3.7: Graphing Linear Inequalities
 Chapter 4: Systems of Equations
 Chapter 4.1: Solving Systems of Linear Equations in Two Variables
 Chapter 4.14.3: Systems of Linear Equations
 Chapter 4.2: Solving Systems of Linear Equations in Three Variables
 Chapter 4.3: Systems of Linear Equations and Problem Solving
 Chapter 4.4: Solving Systems of Equations by Matrices
 Chapter 4.5: Systems of Linear Inequalities
 Chapter 5: Exponents, Polynomials, and Polynomial Functions
 Chapter 5.1: Exponents and Scientific Notation
 Chapter 5.155.7: OPERATIONS ON POLYNOMIALS AND FACTORING STRATEGIES
 Chapter 5.2: More Work with Exponents and Scientific Notation
 Chapter 5.3: Polynomials and Polynomial Functions
 Chapter 5.4: Multiplying Polynomials
 Chapter 5.5: The Greatest Common Factor and Factoring by Grouping
 Chapter 5.6: Factoring Trinomials
 Chapter 5.7: Factoring by Special Products
 Chapter 5.8: Solving Equations by Factoring and Problem Solving
 Chapter 6: Rational Expressions
 Chapter 6.1: Rational Functions and Multiplying and Dividing Rational Expressions
 Chapter 6.2: Adding and Subtracting Rational Expressions
 Chapter 6.3: Simplifying Complex Fractions
 Chapter 6.4: Dividing Polynomials: Long Division and Synthetic Division
 Chapter 6.5: Solving Equations Containing Rational Expressions
 Chapter 6.6: Rational Equations and Problem Solving
 Chapter 6.7: Variation and Problem Solving
 Chapter 7: Rational Exponents, Radicals, and Complex Numbers
 Chapter 7.1: Radicals and Radical Functions
 Chapter 7.17.5: Radical Equations and Problem Solving
 Chapter 7.2: Rational Exponents
 Chapter 7.3: Simplifying Radical Expressions
 Chapter 7.4: Adding, Subtracting, and Multiplying Radical Expressions
 Chapter 7.5: Rationalizing Denominators and Numerators of Radical Expressions
 Chapter 7.6: Radical Equations and Problem Solving
 Chapter 7.7: Complex Numbers
 Chapter 8: Quadratic Equations and Functions
 Chapter 8.1: Solving Quadratic Equations by Completing the Square
 Chapter 8.18.3: SUMMARY ON SOLVING QUADRATIC EQUATIONS
 Chapter 8.2: Solving Quadratic Equations by the Quadratic Formula
 Chapter 8.3: Solving Equations by Using Quadratic Methods
 Chapter 8.4: Nonlinear Inequalities in One Variable
 Chapter 8.5: Quadratic Functions and Their Graphs
 Chapter 8.6: Further Graphing of Quadratic Functions
 Chapter 9: Exponential and Logarithmic Functions
 Chapter 9.1: The Algebra of Functions; Composite Functions
 Chapter 9.19.6: FUNCTIONS AND PROPERTIES OF LOGARITHMS
 Chapter 9.2: Inverse Functions
 Chapter 9.3: Exponential Functions
 Chapter 9.4: Exponential Growth and Decay Functions
 Chapter 9.5: Logarithmic Functions
 Chapter 9.6: Properties of Logarithms
 Chapter 9.7: Common Logarithms, Natural Logarithms, and Change of Base
 Chapter 9.8: Exponential and Logarithmic Equations and Problem Solving
 Chapter Appendix A:
 Chapter Appendix B:
 Chapter Appendix C:
 Chapter Appendix D:
Intermediate Algebra 6th Edition  Solutions by Chapter
Full solutions for Intermediate Algebra  6th Edition
ISBN: 9780321785046
Intermediate Algebra  6th Edition  Solutions by Chapter
Get Full SolutionsThis textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. The full stepbystep solution to problem in Intermediate Algebra were answered by , our top Math solution expert on 12/23/17, 04:59PM. Since problems from 90 chapters in Intermediate Algebra have been answered, more than 94886 students have viewed full stepbystep answer. This expansive textbook survival guide covers the following chapters: 90. Intermediate Algebra was written by and is associated to the ISBN: 9780321785046.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

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

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

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.

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.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex 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.

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.

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

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Outer product uv T
= column times row = rank one matrix.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

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).

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Solvable system Ax = b.
The right side b is in the column space of A.