 4.1.1: Graphy = 2x  3
 4.1.2: Find the slope of the line joining the points 2, 5 and11, 32.
 4.1.3: Find the average rate of change of from 2 to 4. f1x2 = 3x2  2
 4.1.4: Solve:60x  900 = 15x + 2850.
 4.1.5: Iff1x2 = x f122.
 4.1.6: True or False The graph of the function f1x2 = x2 is increasing on ...
 4.1.7: For the graph of the linear function f1x2 = mx + b, m is the and b ...
 4.1.8: For the graph of the linear function H1z2 = 4z + 3 the slope is an...
 4.1.9: If the slope m of the graph of a linear function is , the function ...
 4.1.10: True or False The slope of a nonvertical line is the average rate o...
 4.1.11: True or False If the average rate of change of a linear function is...
 4.1.12: True or False The average rate of change of f1x2 = 2x + 8 is 8.
 4.1.13: In 1320, a linear function is given. (a) Determine the slope and y...
 4.1.14: In 1320, a linear function is given. (a) Determine the slope and y...
 4.1.15: In 1320, a linear function is given. (a) Determine the slope and y...
 4.1.16: In 1320, a linear function is given. (a) Determine the slope and y...
 4.1.17: In 1320, a linear function is given. (a) Determine the slope and y...
 4.1.18: In 1320, a linear function is given. (a) Determine the slope and y...
 4.1.19: In 1320, a linear function is given. (a) Determine the slope and y...
 4.1.20: In 1320, a linear function is given. (a) Determine the slope and y...
 4.1.21: In 2128, determine whether the given function is linear or nonlinea...
 4.1.22: In 2128, determine whether the given function is linear or nonlinea...
 4.1.23: In 2128, determine whether the given function is linear or nonlinea...
 4.1.24: In 2128, determine whether the given function is linear or nonlinea...
 4.1.25: In 2128, determine whether the given function is linear or nonlinea...
 4.1.26: In 2128, determine whether the given function is linear or nonlinea...
 4.1.27: In 2128, determine whether the given function is linear or nonlinea...
 4.1.28: In 2128, determine whether the given function is linear or nonlinea...
 4.1.29: Suppose that and (a) Solve (b) Solve (c) Solve (d) Solve (e) Graph ...
 4.1.30: (a) Solve (b) Solve (c) Solve (d) Solve (e) Graph and and label the...
 4.1.31: In parts (a)(f), use the following figure.
 4.1.32: In parts (a)(f), use the following figure.
 4.1.33: In parts (a) and (b) use the following figure.
 4.1.34: In parts (a) and (b), use the following figure.
 4.1.35: In parts (a) and (b), use the following figure.
 4.1.36: In parts (a) and (b), use the following figure.
 4.1.37: Car Rentals The cost C,in dollars,ofrenting a moving truck for a da...
 4.1.38: Phone Charges The monthly cost C, in dollars, for international cal...
 4.1.39: Supply and Demand Suppose that the quantity supplied S and quantity...
 4.1.40: Supply and Demand Suppose that the quantity supplied S and quantity...
 4.1.41: Taxes The function T1x2 = 0.151x  83502 + 835 represents the tax b...
 4.1.42: Luxury Tax In 2002, major league baseball signed a labor agreement ...
 4.1.43: R1x2 = 8x C1x2 = 4.5x + 17,500
 4.1.44: R1x2 = 12x C1x2 = 10x + 15,000
 4.1.45: Straightline Depreciation Suppose that a company has just purchase...
 4.1.46: Straightline Depreciation Suppose that a company has just purchase...
 4.1.47: Cost Function The simplest cost function is the linear cost functio...
 4.1.48: Cost Function Refer to 47. Suppose that the landlord of the buildin...
 4.1.49: Truck Rentals A truck rental company rents a truck for one day by c...
 4.1.50: Long Distance A phone company offers a domestic long distance packa...
 4.1.51: Developing a Linear Model from Data The following data represent th...
 4.1.52: Developing a Linear Model from Data The following data represent th...
 4.1.53: Which of the following functions might have the graph shown? (More ...
 4.1.54: Which of the following functions might have the graph shown? (More ...
 4.1.55: Under what circumstances is a linear function f1x2 = mx + b odd? Ca...
 4.1.56: Explain how the graph of f1x2 = mx + b can be used to solve mx + b ...
Solutions for Chapter 4.1: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 4.1
Get Full SolutionsSince 56 problems in chapter 4.1 have been answered, more than 58154 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9. Algebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 4.1 includes 56 full stepbystep solutions.

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.

Column space C (A) =
space of all combinations of the columns of A.

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

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex 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.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

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

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).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Outer product uv T
= column times row = rank one matrix.

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).

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Solvable system Ax = b.
The right side b is in the column space of A.

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.