 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 244155 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.

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

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).

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.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

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 edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Iterative method.
A sequence of steps intended to approach the desired solution.

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.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

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).

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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.

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).

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

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

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.