 4.2.1: Explain how to find the input variable in a word problem that uses ...
 4.2.2: Explain how to find the output variable in a word problem that uses...
 4.2.3: Explain how to interpret the initial value in a word problem that u...
 4.2.4: Explain how to determine the slope in a word problem that uses a li...
 4.2.5: Find the area of a parallelogram bounded by the yaxis, the line x ...
 4.2.6: Find the area of a triangle bounded by the xaxis, the line f(x) = ...
 4.2.7: Find the area of a triangle bounded by the yaxis, the line f(x) = ...
 4.2.8: Find the area of a parallelogram bounded by the xaxis, the line g(...
 4.2.9: For the following exercises, consider this scenario: A towns popula...
 4.2.10: For the following exercises, consider this scenario: A towns popula...
 4.2.11: For the following exercises, consider this scenario: A towns popula...
 4.2.12: For the following exercises, consider this scenario: A towns popula...
 4.2.13: For the following exercises, consider this scenario: A town has an ...
 4.2.14: For the following exercises, consider this scenario: A town has an ...
 4.2.15: For the following exercises, consider this scenario: A town has an ...
 4.2.16: For the following exercises, consider this scenario: A town has an ...
 4.2.17: For the following exercises, consider this scenario: A town has an ...
 4.2.18: For the following exercises, consider this scenario: A town has an ...
 4.2.19: For the following exercises, consider this scenario: The weight of ...
 4.2.20: For the following exercises, consider this scenario: The weight of ...
 4.2.21: For the following exercises, consider this scenario: The weight of ...
 4.2.22: For the following exercises, consider this scenario: The weight of ...
 4.2.23: For the following exercises, consider this scenario: The weight of ...
 4.2.24: For the following exercises, consider this scenario: The weight of ...
 4.2.25: For the following exercises, consider this scenario: The number of ...
 4.2.26: For the following exercises, consider this scenario: The number of ...
 4.2.27: For the following exercises, consider this scenario: The number of ...
 4.2.28: For the following exercises, consider this scenario: The number of ...
 4.2.29: For the following exercises, consider this scenario: The number of ...
 4.2.30: For the following exercises, consider this scenario: The number of ...
 4.2.31: For the following exercises, use the graph in Figure 7, which shows...
 4.2.32: For the following exercises, use the graph in Figure 7, which shows...
 4.2.33: For the following exercises, use the graph in Figure 7, which shows...
 4.2.34: For the following exercises, use the graph in Figure 7, which shows...
 4.2.35: For the following exercises, use the graph in Figure 8, which shows...
 4.2.36: For the following exercises, use the graph in Figure 8, which shows...
 4.2.37: For the following exercises, use the graph in Figure 8, which shows...
 4.2.38: For the following exercises, use the graph in Figure 8, which shows...
 4.2.39: For the following exercises, use the median home values in Mississi...
 4.2.40: For the following exercises, use the median home values in Mississi...
 4.2.41: If we assume the linear trend existed before 1950 and continues aft...
 4.2.42: For the following exercises, use the median home values in Indiana ...
 4.2.43: For the following exercises, use the median home values in Indiana ...
 4.2.44: For the following exercises, use the median home values in Indiana ...
 4.2.45: In 2004, a school population was 1,001. By 2008 the population had ...
 4.2.46: In 2003, a towns population was 1,431. By 2007 the population had g...
 4.2.47: A phone company has a monthly cellular plan where a customer pays a...
 4.2.48: A phone company has a monthly cellular data plan where a customer p...
 4.2.49: In 1991, the moose population in a park was measured to be 4,360. B...
 4.2.50: In 2003, the owl population in a park was measured to be 340. By 20...
 4.2.51: The Federal Helium Reserve held about 16 billion cubic feet of heli...
 4.2.52: Suppose the worlds oil reserves in 2014 are 1,820 billion barrels. ...
 4.2.53: You are choosing between two different prepaid cell phone plans. Th...
 4.2.54: You are choosing between two different window washing companies. Th...
 4.2.55: When hired at a new job selling jewelry, you are given two pay opti...
 4.2.56: When hired at a new job selling electronics, you are given two pay ...
 4.2.57: When hired at a new job selling electronics, you are given two pay ...
 4.2.58: When hired at a new job selling electronics, you are given two pay ...
Solutions for Chapter 4.2: MODELING WITH LINEAR FUNCTIONS
Full solutions for College Algebra  1st Edition
ISBN: 9781938168383
Solutions for Chapter 4.2: MODELING WITH LINEAR FUNCTIONS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 58 problems in chapter 4.2: MODELING WITH LINEAR FUNCTIONS have been answered, more than 30309 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra, edition: 1. College Algebra was written by and is associated to the ISBN: 9781938168383. Chapter 4.2: MODELING WITH LINEAR FUNCTIONS includes 58 full stepbystep solutions.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

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

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. 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.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

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.

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

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

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.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·