 5.5.1: Fill in each blank so that the resulting statement is true.The orde...
 5.5.2: Fill in each blank so that the resulting statement is true.The set ...
 5.5.3: Fill in each blank so that the resulting statement is true.The set ...
 5.5.4: Fill in each blank so that the resulting statement is true.True or ...
 5.5.5: Fill in each blank so that the resulting statement is true.True or ...
 5.5.6: Fill in each blank so that the resulting statement is true.True or ...
 5.5.7: Fill in each blank so that the resulting statement is true.When gra...
 5.5.8: Fill in each blank so that the resulting statement is true.The solu...
 5.5.9: Fill in each blank so that the resulting statement is true.True or ...
 5.5.10: In Exercises 126, graph each inequality.x 3
 5.5.11: In Exercises 126, graph each inequality.y 7 1
 5.5.12: In Exercises 126, graph each inequality.y 7 3
 5.5.13: In Exercises 126, graph each inequality.x2 + y2 1
 5.5.14: In Exercises 126, graph each inequality.x2 + y2 4
 5.5.15: In Exercises 126, graph each inequality.x2 + y2 7 25
 5.5.16: In Exercises 126, graph each inequality.x2 + y2 7 36
 5.5.17: In Exercises 126, graph each inequality.(x  2)2 + (y + 1)2 6 9
 5.5.18: In Exercises 126, graph each inequality.(x + 2)2 + (y  1)2 6 16
 5.5.19: In Exercises 126, graph each inequality.y 6 x2  1
 5.5.20: In Exercises 126, graph each inequality.y 6 x2  9
 5.5.21: In Exercises 126, graph each inequality.y x2  9
 5.5.22: In Exercises 126, graph each inequality.y x2  1
 5.5.23: In Exercises 126, graph each inequality.y 7 2x
 5.5.24: In Exercises 126, graph each inequality.y 3x
 5.5.25: In Exercises 126, graph each inequality.y log2(x + 1)
 5.5.26: In Exercises 126, graph each inequality.y log3(x  1)
 5.5.27: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.28: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.29: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.30: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.31: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.32: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.33: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.34: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.35: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.36: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.37: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.38: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.39: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.40: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.41: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.42: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.43: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.44: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.45: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.46: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.47: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.48: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.49: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.50: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.51: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.52: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.53: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.54: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.55: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.56: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.57: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.58: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.59: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.60: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.61: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.62: In Exercises 2762, graph the solution set of each system ofinequali...
 5.5.63: In Exercises 6364, write each sentence as an inequality in twovaria...
 5.5.64: In Exercises 6364, write each sentence as an inequality in twovaria...
 5.5.65: In Exercises 6568, write the given sentences as a system ofinequali...
 5.5.66: In Exercises 6568, write the given sentences as a system ofinequali...
 5.5.67: In Exercises 6568, write the given sentences as a system ofinequali...
 5.5.68: In Exercises 6568, write the given sentences as a system ofinequali...
 5.5.69: In Exercises 6970, rewrite each inequality in the systemwithout abs...
 5.5.70: In Exercises 6970, rewrite each inequality in the systemwithout abs...
 5.5.71: The graphs of solution sets of systems of inequalities involvefindi...
 5.5.72: The graphs of solution sets of systems of inequalities involvefindi...
 5.5.73: Without graphing, in Exercises 7376, determine if each systemhas no...
 5.5.74: Without graphing, in Exercises 7376, determine if each systemhas no...
 5.5.75: Without graphing, in Exercises 7376, determine if each systemhas no...
 5.5.76: Without graphing, in Exercises 7376, determine if each systemhas no...
 5.5.77: The figure shows the healthy weight region for various heights forp...
 5.5.78: The figure shows the healthy weight region for various heights forp...
 5.5.79: The figure shows the healthy weight region for various heights forp...
 5.5.80: The figure shows the healthy weight region for various heights forp...
 5.5.81: Many elevators have a capacity of 2000 pounds.a. If a child average...
 5.5.82: A patient is not allowed to have more than 330 milligrams ofcholest...
 5.5.83: On your next vacation, you will divide lodging between largeresorts...
 5.5.84: A person with no more than $15,000 to invest plans to placethe mone...
 5.5.85: The graph of an inequality in two variables is a region in the rect...
 5.5.86: The graph of an inequality in two variables is a region in the rect...
 5.5.87: What is a linear inequality in two variables? Provide anexample wit...
 5.5.88: How do you determine if an ordered pair is a solution of aninequali...
 5.5.89: What is a halfplane?
 5.5.90: What does a solid line mean in the graph of an inequality?
 5.5.91: What does a dashed line mean in the graph of an inequality?
 5.5.92: Compare the graphs of 3x  2y 7 6 and 3x  2y 6.Discuss similaritie...
 5.5.93: What is a system of linear inequalities?
 5.5.94: What is a solution of a system of linear inequalities?
 5.5.95: Explain how to graph the solution set of a system of inequalities.
 5.5.96: What does it mean if a system of linear inequalities has nosolution?
 5.5.97: Graphing utilities can be used to shade regions in the rectangularc...
 5.5.98: Graphing utilities can be used to shade regions in the rectangularc...
 5.5.99: Graphing utilities can be used to shade regions in the rectangularc...
 5.5.100: Graphing utilities can be used to shade regions in the rectangularc...
 5.5.101: Graphing utilities can be used to shade regions in the rectangularc...
 5.5.102: Graphing utilities can be used to shade regions in the rectangularc...
 5.5.103: Does your graphing utility have any limitations in terms ofgraphing...
 5.5.104: Use a graphing utility to verify any five of the graphs thatyou dre...
 5.5.105: Use a graphing utility to verify any five of the graphs thatyou dre...
 5.5.106: In Exercises 106109, determine whether eachstatement makes sense or...
 5.5.107: In Exercises 106109, determine whether eachstatement makes sense or...
 5.5.108: In Exercises 106109, determine whether eachstatement makes sense or...
 5.5.109: In Exercises 106109, determine whether eachstatement makes sense or...
 5.5.110: In Exercises 110113, write a system of inequalities for each graph.110
 5.5.111: In Exercises 110113, write a system of inequalities for each graph.111
 5.5.112: In Exercises 110113, write a system of inequalities for each graph.112
 5.5.113: In Exercises 110113, write a system of inequalities for each graph.113
 5.5.114: Write a system of inequalities whose solution set includesevery poi...
 5.5.115: Sketch the graph of the solution set for the following systemof ine...
 5.5.116: Let f(x) = bx + 3 if x 58 if x 6 5.Find f(12)  f(12). (Section 2....
 5.5.117: Solve and graph the solution set on a number line:x  2x  1 1.(Sec...
 5.5.118: The functionf(t) = 25.11 + 2.7e 0.05tmodels the population of Flor...
 5.5.119: Exercises 119121 will help you prepare for the material coveredin t...
 5.5.120: Exercises 119121 will help you prepare for the material coveredin t...
 5.5.121: Exercises 119121 will help you prepare for the material coveredin t...
Solutions for Chapter 5.5: Systems of Inequalities
Full solutions for College Algebra  7th Edition
ISBN: 9780134469164
Solutions for Chapter 5.5: Systems of Inequalities
Get Full SolutionsChapter 5.5: Systems of Inequalities includes 121 full stepbystep solutions. College Algebra was written by and is associated to the ISBN: 9780134469164. Since 121 problems in chapter 5.5: Systems of Inequalities have been answered, more than 32543 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra , edition: 7. This expansive textbook survival guide covers the following chapters and their solutions.

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

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

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

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].

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.

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.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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

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

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

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 N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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).

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

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

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.