 3.7.1: What type of model best represents data that follow a parabolic pat...
 3.7.2: Which coefficient of determination indicates a better model for a s...
 3.7.3: In Exercises 3 8, determine whether the scatter plot could best be ...
 3.7.4: In Exercises 3 8, determine whether the scatter plot could best be ...
 3.7.5: In Exercises 3 8, determine whether the scatter plot could best be ...
 3.7.6: In Exercises 3 8, determine whether the scatter plot could best be ...
 3.7.7: In Exercises 3 8, determine whether the scatter plot could best be ...
 3.7.8: In Exercises 3 8, determine whether the scatter plot could best be ...
 3.7.9: In Exercises 916, (a) use a graphing utility to create a scatter pl...
 3.7.10: In Exercises 916, (a) use a graphing utility to create a scatter pl...
 3.7.11: In Exercises 916, (a) use a graphing utility to create a scatter pl...
 3.7.12: In Exercises 916, (a) use a graphing utility to create a scatter pl...
 3.7.13: In Exercises 916, (a) use a graphing utility to create a scatter pl...
 3.7.14: In Exercises 916, (a) use a graphing utility to create a scatter pl...
 3.7.15: In Exercises 916, (a) use a graphing utility to create a scatter pl...
 3.7.16: In Exercises 916, (a) use a graphing utility to create a scatter pl...
 3.7.17: The table shows the monthly normal precipitation P (in inches) for ...
 3.7.18: The table shows the annual sales S (in billions of dollars) of phar...
 3.7.19: The table shows the percents P of U.S. households with Internet acc...
 3.7.20: The table shows the estimated average numbers of hours H that adult...
 3.7.21: The table shows the numbers of U.S. households with televisions (in...
 3.7.22: In Exercises 2224, determine whether the statement is true or false...
 3.7.23: In Exercises 2224, determine whether the statement is true or false...
 3.7.24: In Exercises 2224, determine whether the statement is true or false...
 3.7.25: Explain why the parabola shown in the figure is not a good fit for ...
 3.7.26: The r2values representing the coefficients of determination for th...
 3.7.27: In Exercises 2730, find (a) f g and (b) g f. 27. f(x) = 2x 1, g(x) ...
 3.7.28: In Exercises 2730, find (a) f g and (b) g f. 27. 28. f(x) = 5x + 8,...
 3.7.29: In Exercises 2730, find (a) f g and (b) g f. 29. f(x) = x3 1, g(x) ...
 3.7.30: In Exercises 2730, find (a) f g and (b) g f.30. f(x) = 3 x + 5, g(x...
 3.7.31: In Exercises 3134, determine algebraically whether the function is ...
 3.7.32: In Exercises 3134, determine algebraically whether the function is ...
 3.7.33: In Exercises 3134, determine algebraically whether the function is ...
 3.7.34: In Exercises 3134, determine algebraically whether the function is ...
 3.7.35: In Exercises 35 38, write the complex conjugate of the complex numb...
 3.7.36: In Exercises 35 38, write the complex conjugate of the complex numb...
 3.7.37: In Exercises 35 38, write the complex conjugate of the complex numb...
 3.7.38: In Exercises 35 38, write the complex conjugate of the complex numb...
Solutions for Chapter 3.7: Polynomial and Rational Functions
Full solutions for Algebra and Trigonometry: Real Mathematics, Real People  7th Edition
ISBN: 9781305071735
Solutions for Chapter 3.7: Polynomial and Rational Functions
Get Full SolutionsChapter 3.7: Polynomial and Rational Functions includes 38 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry: Real Mathematics, Real People, edition: 7. Algebra and Trigonometry: Real Mathematics, Real People was written by and is associated to the ISBN: 9781305071735. Since 38 problems in chapter 3.7: Polynomial and Rational Functions have been answered, more than 59024 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

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

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

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

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.

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 .

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.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

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

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

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

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.