- Chapter 1: Equations, Inequalities, and Mathematical Modeling
- Chapter 1.1: Graphs of Equations
- Chapter 1.2: Linear Equations in One Variable
- Chapter 1.3: Modeling with Linear Equations
- Chapter 1.4: Quadratic Equations and Applications
- Chapter 1.5: Complex Numbers
- Chapter 1.6: Other Types of Equations
- Chapter 1.7: Linear Inequalities in One Variable
- Chapter 1.8: Other Types of Inequalities
- Chapter 10: Matrices and Determinants
- Chapter 10.1: Matrices and Systems of Equations
- Chapter 10.2: Operations with Matrices
- Chapter 10.3: The Inverse of a Square Matrix
- Chapter 10.4: The Determinant of a Square Matrix
- Chapter 10.5: Applications of Matrices and Determinants
- Chapter 11: Sequences, Series and Probability
- Chapter 11.1: Sequences and Series
- Chapter 11.2: Arithmetic Sequences and Partial Sums
- Chapter 11.3: Geometric Sequences and Series
- Chapter 11.4: Mathematical Induction
- Chapter 11.5: The Binomial Theorem
- Chapter 11.6: Counting Principles
- Chapter 11.7: Probability
- Chapter 2: Functions and Their Graphs
- Chapter 2.1: Linear Equations in Two Variables
- Chapter 2.2: Functions
- Chapter 2.3: Analyzing Graphs of Functions
- Chapter 2.4: A Library of Parent Functions
- Chapter 2.5: Transformations of Functions
- Chapter 2.6: Combinations of Functions: Composite Functions
- Chapter 2.7: Inverse Functions
- Chapter 3: Polynomial Functions
- Chapter 3.1: Quadratic Functions and Models
- Chapter 3.2: Polynomial Functions of Higher Degree
- Chapter 3.3: Polynomial and Synthetic Division
- Chapter 3.4: Zeros of Polynomial Functions
- Chapter 3.5: Mathematical Modeling and Variation
- Chapter 4: Rational Functions and Conics
- Chapter 4.1: Rational Functions and Asymptotes
- Chapter 4.2: Graphs of Rational Functions
- Chapter 4.3: Conics
- Chapter 4.4: Translations of Conics
- Chapter 5: Exponential and Logarithmic Functions
- Chapter 5.1: Exponential Functions and Their Graphs
- Chapter 5.2: Logarithmic Functions and Their Graphs
- Chapter 5.3: Properties of Logarithms
- Chapter 5.4: Exponential and Logarithmic Equations
- Chapter 5.5: Exponential and Logarithmic Models
- Chapter 6: Trigonometry
- Chapter 6.1: Angles and Their Measure
- Chapter 6.2: Right Triangle Trigonometry
- Chapter 6.3: Trigonometric Functions of Any Angle
- Chapter 6.4: Graphs of Sine and Cosine Functions
- Chapter 6.5: Graphs of Trigonometric Functions
- Chapter 6.6: Inverse Trigonometric Functions
- Chapter 6.7: Applications and Models
- Chapter 7: Analytic Trigonometry
- Chapter 7.1: Using Fundamental Identities
- Chapter 7.2: Verifying Trigonometric Identities
- Chapter 7.3: Solving Trigonometric Equations
- Chapter 7.4: Sum and Difference Formulas
- Chapter 7.5: Multiple-Angle and Product-to-Sum Formulas
- Chapter 8: Additional Topics in Trigonometry
- Chapter 8.1: Law of Sines
- Chapter 8.2: Law of Cosines
- Chapter 8.3: Vectors in The Plane
- Chapter 8.4: Vectors and Dot Products
- Chapter 8.5: Trigonometric Form of A Complex Number
- Chapter 9: Systems of Equations and Inequlities
- Chapter 9.1: Linear and Nonlinear Systems of Equations
- Chapter 9.2: Two-Variable Linear Systems
- Chapter 9.3: Multivariable Linear Systems
- Chapter 9.4: Partial Fractions
- Chapter 9.5: Systems of Inequalities
- Chapter 9.6: Linear Programming
- Chapter A: Appendix A Errors and the Algebra of Calculus
- Chapter P: Prerequisites
- Chapter P.1: Review of Real Numbers and Their Properties
- Chapter P.2: Exponents and Radicals
- Chapter P.3: Polynomials and Special Products
- Chapter P.4: Factoring Polynomials
- Chapter P.5: Rational Expressions
- Chapter P.6: The Rectangular Coordinate System and Graphs
Algebra and Trigonometry 8th Edition - Solutions by Chapter
Full solutions for Algebra and Trigonometry | 8th Edition
ISBN: 9781439048474
Solutions by Chapter
Since problems from 83 chapters in Algebra and Trigonometry have been answered, more than 83208 students have viewed full step-by-step answer. The full step-by-step solution to problem in Algebra and Trigonometry were answered by , our top Math solution expert on 12/27/17, 07:37PM. This expansive textbook survival guide covers the following chapters: 83. Algebra and Trigonometry was written by and is associated to the ISBN: 9781439048474. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8.
Key Math Terms and definitions covered in this textbook
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Cayley-Hamilton Theorem.
peA) = det(A - AI) has peA) = zero matrix.
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Complex conjugate
z = a - ib for any complex number z = a + ib. Then zz = Iz12.
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Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA-1 yll2 = Y T(AAT)-1 Y = 1 displayed by eigshow; axis lengths ad
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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.
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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.
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Gauss-Jordan method.
Invert A by row operations on [A I] to reach [I A-I].
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Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.
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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.
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lA-II = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n - 1, volume of box = I det( A) I.
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Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.
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Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Q-l. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.
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Outer product uv T
= column times row = rank one matrix.
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Row space C (AT) = all combinations of rows of A.
Column vectors by convention.
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Singular matrix A.
A square matrix that has no inverse: det(A) = o.
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Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.
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Special solutions to As = O.
One free variable is Si = 1, other free variables = o.
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Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.
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Tridiagonal matrix T: tij = 0 if Ii - j I > 1.
T- 1 has rank 1 above and below diagonal.
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Unitary matrix UH = U T = U-I.
Orthonormal columns (complex analog of Q).
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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.