 1.1.1: True or False On the real number line, the coordinate of the origin...
 1.1.2: Solve the equation: 2x + 6 = 10
 1.1.3: True or False To find the yintercept of a linear equation, let and...
 1.1.4: The equation of a vertical line with xintercept at is_____.
 1.1.5: If the slope of a line is undefined, the line is _____.
 1.1.6: The line has slope _____ and yintercept_____.
 1.1.7: The pointslope form of the equation of a line with slope m containi...
 1.1.8: If the graph of a line slants downward from left to right, its slop...
 1.1.9: Give the coordinates of each point in the following figure. Assume ...
 1.1.10: Plot each point in the xyplane. Tell in which quadrant or on what ...
 1.1.11: Plot the points (2, 0), (2, 4), (2, 1), and Describe the collection...
 1.1.12: Plot the points (0, 3), (1, 3), (5, 3), and Describe the collection...
 1.1.13: In 1316, use the given equation to fill in the missing values in ea...
 1.1.14: In 1316, use the given equation to fill in the missing values in ea...
 1.1.15: In 1316, use the given equation to fill in the missing values in ea...
 1.1.16: In 1316, use the given equation to fill in the missing values in ea...
 1.1.17: In 1722 a point is given. (a) Find the equation of the vertical lin...
 1.1.18: In 1722 a point is given. (a) Find the equation of the vertical lin...
 1.1.19: In 1722 a point is given. (a) Find the equation of the vertical lin...
 1.1.20: In 1722 a point is given. (a) Find the equation of the vertical lin...
 1.1.21: In 1722 a point is given. (a) Find the equation of the vertical lin...
 1.1.22: In 1722 a point is given. (a) Find the equation of the vertical lin...
 1.1.23: In 2326, find the slope of the line. Give an interpretation of the ...
 1.1.24: In 2326, find the slope of the line. Give an interpretation of the ...
 1.1.25: In 2326, find the slope of the line. Give an interpretation of the ...
 1.1.26: In 2326, find the slope of the line. Give an interpretation of the ...
 1.1.27: In 2734, plot each pair of points and find the slope of the line co...
 1.1.28: In 2734, plot each pair of points and find the slope of the line co...
 1.1.29: In 2734, plot each pair of points and find the slope of the line co...
 1.1.30: In 2734, plot each pair of points and find the slope of the line co...
 1.1.31: In 2734, plot each pair of points and find the slope of the line co...
 1.1.32: In 2734, plot each pair of points and find the slope of the line co...
 1.1.33: In 2734, plot each pair of points and find the slope of the line co...
 1.1.34: In 2734, plot each pair of points and find the slope of the line co...
 1.1.35: In 3542, graph the line containing the point P and having slope m. ...
 1.1.36: In 3542, graph the line containing the point P and having slope m. ...
 1.1.37: In 3542, graph the line containing the point P and having slope m. ...
 1.1.38: In 3542, graph the line containing the point P and having slope m. ...
 1.1.39: In 3542, graph the line containing the point P and having slope m. ...
 1.1.40: In 3542, graph the line containing the point P and having slope m. ...
 1.1.41: In 3542, graph the line containing the point P and having slope m. ...
 1.1.42: In 3542, graph the line containing the point P and having slope m. ...
 1.1.43: In 4364, find the general equation of each line; that is, write the...
 1.1.44: In 4364, find the general equation of each line; that is, write the...
 1.1.45: In 4364, find the general equation of each line; that is, write the...
 1.1.46: In 4364, find the general equation of each line; that is, write the...
 1.1.47: In 4364, find the general equation of each line; that is, write the...
 1.1.48: In 4364, find the general equation of each line; that is, write the...
 1.1.49: In 4364, find the general equation of each line; that is, write the...
 1.1.50: In 4364, find the general equation of each line; that is, write the...
 1.1.51: In 4364, find the general equation of each line; that is, write the...
 1.1.52: In 4364, find the general equation of each line; that is, write the...
 1.1.53: In 4364, find the general equation of each line; that is, write the...
 1.1.54: In 4364, find the general equation of each line; that is, write the...
 1.1.55: In 4364, find the general equation of each line; that is, write the...
 1.1.56: In 4364, find the general equation of each line; that is, write the...
 1.1.57: In 4364, find the general equation of each line; that is, write the...
 1.1.58: In 4364, find the general equation of each line; that is, write the...
 1.1.59: In 4364, find the general equation of each line; that is, write the...
 1.1.60: In 4364, find the general equation of each line; that is, write the...
 1.1.61: In 4364, find the general equation of each line; that is, write the...
 1.1.62: In 4364, find the general equation of each line; that is, write the...
 1.1.63: In 4364, find the general equation of each line; that is, write the...
 1.1.64: In 4364, find the general equation of each line; that is, write the...
 1.1.65: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.66: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.67: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.68: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.69: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.70: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.71: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.72: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.73: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.74: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.75: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.76: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.77: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.78: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.79: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.80: In 6580, find the slope and yintercept of each line. Graph the lin...
 1.1.81: In 8188, use a graphing utility to graph each linear equation. Be s...
 1.1.82: In 8188, use a graphing utility to graph each linear equation. Be s...
 1.1.83: In 8188, use a graphing utility to graph each linear equation. Be s...
 1.1.84: In 8188, use a graphing utility to graph each linear equation. Be s...
 1.1.85: In 8188, use a graphing utility to graph each linear equation. Be s...
 1.1.86: In 8188, use a graphing utility to graph each linear equation. Be s...
 1.1.87: In 8188, use a graphing utility to graph each linear equation. Be s...
 1.1.88: In 8188, use a graphing utility to graph each linear equation. Be s...
 1.1.89: In 8992, match each graph with the correct equation: y = x y = 2x y...
 1.1.90: In 8992, match each graph with the correct equation: y = x y = 2x y...
 1.1.91: In 8992, match each graph with the correct equation: y = x y = 2x y...
 1.1.92: In 8992, match each graph with the correct equation: y = x y = 2x y...
 1.1.93: In 9396, write an equation of each line. Express your answer using ...
 1.1.94: In 9396, write an equation of each line. Express your answer using ...
 1.1.95: In 9396, write an equation of each line. Express your answer using ...
 1.1.96: In 9396, write an equation of each line. Express your answer using ...
 1.1.97: Cost of Operating a Car According to the American Automobile Associ...
 1.1.98: Cost of Renting a Truck In January 2010, the cost of renting a truc...
 1.1.99: Electricity Rates in Illinois Commonwealth Edison Company supplies ...
 1.1.100: Electricity Rates in Florida Florida Power & Light Company supplies...
 1.1.101: Temperature Conversion The relationship between Celsius (C) and Fah...
 1.1.102: Temperature Conversion The Kelvin (K) scale for measuring temperatu...
 1.1.103: Water Preservation At Harlan County Dam in Nebraska, the U.S. Burea...
 1.1.104: Product Promotion A cereal company finds that the number of people ...
 1.1.105: Predicting Sales Suppose the sales of a company are given by where ...
 1.1.106: Disease Propagation Research indicates that in a controlled environ...
 1.1.107: Wages of a Car Salesperson In 2008, median earnings, including comm...
 1.1.108: Oil Depletion The Alaskan oil fields, in operation since 1977, had ...
 1.1.109: SAT Scores The average score on the mathematics portion of the SAT ...
 1.1.110: Financial Statement In November 2005, SBC Communications acquired A...
 1.1.111: Percent of Population with Bachelors Degrees In 1998 the percent of...
 1.1.112: College Degrees In 2000, 1,237,875 bachelors degrees were conferred...
 1.1.113: Predicting the Cost of a Home In 2008, the average cost of a home i...
 1.1.114: WeightHeight Relation in the U.S.Army Assume the recommended weight...
 1.1.115: Predicting Sales The total sales and other operating income for Che...
 1.1.116: Predicting Revenue The net revenue for Dell, Inc. for the fiscal ye...
 1.1.117: Cost of Gasoline The average price of a gallon of regular gasoline ...
 1.1.118: Cost of Gasoline Repeat parts (a)(e) of for the Jones family who dr...
 1.1.119: Credit and Debit Card Growth At the end of the first quarter of 200...
 1.1.120: Which of the following equations might have the graph shown? (More ...
 1.1.121: Which of the following equations might have the graph shown. (More ...
 1.1.122: Which form of the equation of a line do you prefer to use? Justify ...
 1.1.123: Can every line be written in slopeintercept form? Explain.
 1.1.124: Does every line have two distinct intercepts? Explain. Are there li...
 1.1.125: What can you say about two lines that have equal slopes and equal y...
 1.1.126: What can you say about two lines with the same xintercept and the ...
 1.1.127: If two lines have the same slope, but different xintercepts, can t...
 1.1.128: If two lines have the same yintercept, but different slopes, can t...
 1.1.129: Can a line have two distinct xintercepts? Can a line have infinite...
 1.1.130: Can a line have no xintercept? Can a line have neither an xinterc...
 1.1.131: The accepted symbol used to denote the slope of a line is the lette...
Solutions for Chapter 1.1: Lines
Full solutions for Finite Mathematics, Binder Ready Version: An Applied Approach  11th Edition
ISBN: 9780470876398
Solutions for Chapter 1.1: Lines
Get Full SolutionsFinite Mathematics, Binder Ready Version: An Applied Approach was written by and is associated to the ISBN: 9780470876398. This textbook survival guide was created for the textbook: Finite Mathematics, Binder Ready Version: An Applied Approach, edition: 11. Since 131 problems in chapter 1.1: Lines have been answered, more than 18160 students have viewed full stepbystep solutions from this chapter. Chapter 1.1: Lines includes 131 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

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

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.

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 .

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

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.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

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

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.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.