 2.1: In Exercises 1 and 2, find the distance between the points whose co...
 2.2: In Exercises 1 and 2, find the distance between the points whose co...
 2.3: In Exercises 3 and 4, find the midpoint of the line segment with th...
 2.4: In Exercises 3 and 4, find the midpoint of the line segment with th...
 2.5: In Exercises 5 to 8, graph each equation by plotting points
 2.6: In Exercises 5 to 8, graph each equation by plotting points
 2.7: In Exercises 5 to 8, graph each equation by plotting points
 2.8: In Exercises 5 to 8, graph each equation by plotting points
 2.9: In Exercises 9 to 12, find the x and yintercepts of the graph of ...
 2.10: In Exercises 9 to 12, find the x and yintercepts of the graph of ...
 2.11: In Exercises 9 to 12, find the x and yintercepts of the graph of ...
 2.12: In Exercises 9 to 12, find the x and yintercepts of the graph of ...
 2.13: In Exercises 13 and 14, determine the center and radius of the circ...
 2.14: In Exercises 13 and 14, determine the center and radius of the circ...
 2.15: In Exercises 15 and 16, find the equation in standard form of the c...
 2.16: In Exercises 15 and 16, find the equation in standard form of the c...
 2.17: In Exercises 17 to 20, determine whether the equation defines y as ...
 2.18: In Exercises 17 to 20, determine whether the equation defines y as ...
 2.19: In Exercises 17 to 20, determine whether the equation defines y as ...
 2.20: In Exercises 17 to 20, determine whether the equation defines y as ...
 2.23: Let f be a piecewisedefined function given by
 2.24: Let f be a piecewisedefined function given by
 2.25: In Exercises 25 to 28, determine the domain of the function represe...
 2.26: In Exercises 25 to 28, determine the domain of the function represe...
 2.27: In Exercises 25 to 28, determine the domain of the function represe...
 2.28: In Exercises 25 to 28, determine the domain of the function represe...
 2.29: Find the values of a in the domain of for which .
 2.30: Find the value of a in the domain of for which
 2.31: In Exercises 31 and 32, graph the given equation.
 2.32: In Exercises 31 and 32, graph the given equation.
 2.33: In Exercises 33 and 34, find the zero or zeros of the given function.
 2.34: In Exercises 33 and 34, find the zero or zeros of the given function.
 2.35: In Exercises 35 and 36, find each function value.
 2.36: In Exercises 35 and 36, find each function value.
 2.37: In Exercises 37 to 40, find the slope of the line between the point...
 2.38: In Exercises 37 to 40, find the slope of the line between the point...
 2.39: In Exercises 37 to 40, find the slope of the line between the point...
 2.40: In Exercises 37 to 40, find the slope of the line between the point...
 2.41: Graph using the slope and yintercept
 2.42: Graph using the slope and yintercept
 2.43: Graph 3x  4y = 8.
 2.44: Graph 2x + 3y = 9
 2.45: Find the equation of the line that passes through the point with co...
 2.46: Find the equation of the line that passes through the point with co...
 2.47: Find the equation of the line that passes through the points with c...
 2.48: Find the equation of the line that passes through the points with c...
 2.49: Find the slopeintercept form of the equation of the line that passe...
 2.50: Find the slopeintercept form of the equation of the line that passe...
 2.51: Find the slopeintercept form of the equation of the line that passe...
 2.52: Find the slopeintercept form of the equation of the line that passe...
 2.53: Sports The speed of a professional golfers swing and the speed of t...
 2.54: Food Science Newer heating elements allow an oven to reach a normal...
 2.55: In Exercises 55 to 60, use the method of completing the square to w...
 2.56: In Exercises 55 to 60, use the method of completing the square to w...
 2.57: In Exercises 55 to 60, use the method of completing the square to w...
 2.58: In Exercises 55 to 60, use the method of completing the square to w...
 2.59: In Exercises 55 to 60, use the method of completing the square to w...
 2.60: In Exercises 55 to 60, use the method of completing the square to w...
 2.61: In Exercises 61 to 64, find the vertex of the graph of the quadrati...
 2.62: In Exercises 61 to 64, find the vertex of the graph of the quadrati...
 2.63: In Exercises 61 to 64, find the vertex of the graph of the quadrati...
 2.64: In Exercises 61 to 64, find the vertex of the graph of the quadrati...
 2.65: In Exercises 65 and 66, find the requested value
 2.66: In Exercises 65 and 66, find the requested value
 2.67: . Height of a Ball A ball is thrown vertically upward with an initi...
 2.68: Delivery Cost A freight company has determined that its cost, in do...
 2.69: Agriculture A farmer wishes to enclose a rectangular region borderi...
 2.70: In Exercises 70 and 71, sketch a graph that is symmetric to the giv...
 2.71: In Exercises 70 and 71, sketch a graph that is symmetric to the giv...
 2.72: In Exercises 72 to 79, determine whether the graph of each equation...
 2.73: In Exercises 72 to 79, determine whether the graph of each equation...
 2.74: In Exercises 72 to 79, determine whether the graph of each equation...
 2.75: In Exercises 72 to 79, determine whether the graph of each equation...
 2.76: In Exercises 72 to 79, determine whether the graph of each equation...
 2.77: In Exercises 72 to 79, determine whether the graph of each equation...
 2.78: In Exercises 72 to 79, determine whether the graph of each equation...
 2.79: In Exercises 72 to 79, determine whether the graph of each equation...
 2.80: In Exercises 80 to 85, sketch the graph of g. a. Find the domain an...
 2.81: In Exercises 80 to 85, sketch the graph of g. a. Find the domain an...
 2.82: In Exercises 80 to 85, sketch the graph of g. a. Find the domain an...
 2.83: In Exercises 80 to 85, sketch the graph of g. a. Find the domain an...
 2.84: In Exercises 80 to 85, sketch the graph of g. a. Find the domain an...
 2.85: In Exercises 80 to 85, sketch the graph of g. a. Find the domain an...
 2.86: In Exercises 86 to 91, use the graph of f shown below to sketch a g...
 2.87: In Exercises 86 to 91, use the graph of f shown below to sketch a g...
 2.88: In Exercises 86 to 91, use the graph of f shown below to sketch a g...
 2.89: In Exercises 86 to 91, use the graph of f shown below to sketch a g...
 2.90: In Exercises 86 to 91, use the graph of f shown below to sketch a g...
 2.91: In Exercises 86 to 91, use the graph of f shown below to sketch a g...
 2.92: In Exercises 92 to 95, use the graph of f shown below to sketch a g...
 2.93: In Exercises 92 to 95, use the graph of f shown below to sketch a g...
 2.94: In Exercises 92 to 95, use the graph of f shown below to sketch a g...
 2.95: In Exercises 92 to 95, use the graph of f shown below to sketch a g...
 2.96: Let and . Find each of the following
 2.97: If , find the difference quotient
 2.98: If , find the difference quotient
 2.99: Ball Rolling on a Ramp The distance traveled by a ball rolling down...
 2.100: If and , find a. b. c. d. ( f g)(x) (g f )(x)
 2.101: If and , find
 2.102: Sports A soccer coach examined the relationship between the speed, ...
 2.103: Physics The rate at which water will escape from the bottom of a ru...
Solutions for Chapter 2: College Algebra and Trigonometry 7th Edition
Full solutions for College Algebra and Trigonometry  7th Edition
ISBN: 9781439048603
Solutions for Chapter 2
Get Full SolutionsCollege Algebra and Trigonometry was written by and is associated to the ISBN: 9781439048603. Chapter 2 includes 101 full stepbystep solutions. This textbook survival guide was created for the textbook: College Algebra and Trigonometry, edition: 7. Since 101 problems in chapter 2 have been answered, more than 5945 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

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

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).

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

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

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.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

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

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.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

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}.

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.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.