- Chapter 1: Equations and Inequalities
- Chapter 2: Functions and Graphs
- Chapter 3: Polynomial and Rational Functions
- Chapter 4: Exponential and Logarithmic Functions
- Chapter 5: Topics in Analytic Geometry
- Chapter 6: Systems of Equations and Inequalities
- Chapter 7: Matrices
- Chapter 8: Sequences, Series and Probability
- Chapter P: Preliminary Concepts
College Algebra 7th Edition - Solutions by Chapter
Full solutions for College Algebra | 7th Edition
ISBN: 9781439048610
Solutions by Chapter
The full step-by-step solution to problem in College Algebra were answered by , our top Math solution expert on 01/02/18, 08:47PM. This textbook survival guide was created for the textbook: College Algebra, edition: 7. Since problems from 9 chapters in College Algebra have been answered, more than 45886 students have viewed full step-by-step answer. This expansive textbook survival guide covers the following chapters: 9. College Algebra was written by and is associated to the ISBN: 9781439048610.
Key Math Terms and definitions covered in this textbook
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Affine transformation
Tv = Av + Vo = linear transformation plus shift.
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Cayley-Hamilton Theorem.
peA) = det(A - AI) has peA) = zero matrix.
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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).
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Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.
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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 n-l - An).
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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.
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Diagonal matrix D.
dij = 0 if i #- j. Block-diagonal: zero outside square blocks Du.
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Eigenvalue A and eigenvector x.
Ax = AX with x#-O so det(A - AI) = o.
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Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.
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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!).
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Gauss-Jordan method.
Invert A by row operations on [A I] to reach [I A-I].
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Identity matrix I (or In).
Diagonal entries = 1, off-diagonal entries = 0.
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Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and - ).
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Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.
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Row space C (AT) = all combinations of rows of A.
Column vectors by convention.
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Similar matrices A and B.
Every B = M-I AM has the same eigenvalues as A.
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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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Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.
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Symmetric matrix A.
The transpose is AT = A, and aU = a ji. A-I is also symmetric.