 6.5.45: 2x y > 26x 3y < 2
 6.5.46: x 7y >5x 2y >6x 5y >3656
 6.5.47: 5x 3y > 9 3xx2x 2y < 4y > y <623
 6.5.48: x 2y < 6 5x 3y > 9
 6.5.49: x > y2x < y 2
 6.5.50: x y2 > 0x y > 2
 6.5.51: x2 y2 36x2 y2 9
 6.5.52: x24xy23y 25 0
 6.5.53: 3x 4 x y <y20
 6.5.54: x < 2y y20 < x y
 6.5.55: In Exercises 5560, use a graphing utility to graph thesolution set ...
 6.5.56: In Exercises 5560, use a graphing utility to graph thesolution set ...
 6.5.57: In Exercises 5560, use a graphing utility to graph thesolution set ...
 6.5.58: In Exercises 5560, use a graphing utility to graph thesolution set ...
 6.5.59: In Exercises 5560, use a graphing utility to graph thesolution set ...
 6.5.60: In Exercises 5560, use a graphing utility to graph thesolution set ...
 6.5.61: In Exercises 6170, derive a set of inequalities to describe theregion.
 6.5.62: In Exercises 6170, derive a set of inequalities to describe theregion.
 6.5.63: In Exercises 6170, derive a set of inequalities to describe theregion.
 6.5.64: In Exercises 6170, derive a set of inequalities to describe theregion.
 6.5.65: In Exercises 6170, derive a set of inequalities to describe theregion.
 6.5.66: In Exercises 6170, derive a set of inequalities to describe theregion.
 6.5.67: In Exercises 6170, derive a set of inequalities to describe theregion.
 6.5.68: In Exercises 6170, derive a set of inequalities to describe theregion.
 6.5.69: In Exercises 6170, derive a set of inequalities to describe theregion.
 6.5.70: In Exercises 6170, derive a set of inequalities to describe theregion.
 6.5.71: SUPPLY AND DEMAND In Exercises 7174, (a) graph thesystems represent...
 6.5.72: SUPPLY AND DEMAND In Exercises 7174, (a) graph thesystems represent...
 6.5.73: SUPPLY AND DEMAND In Exercises 7174, (a) graph thesystems represent...
 6.5.74: SUPPLY AND DEMAND In Exercises 7174, (a) graph thesystems represent...
 6.5.75: PRODUCTION A furniture company can sell all thetables and chairs it...
 6.5.76: INVENTORY A store sells two models of laptopcomputers. Because of t...
 6.5.77: INVESTMENT ANALYSIS A person plans to invest upto $20,000 in two di...
 6.5.78: TICKET SALES For a concert event, there are $30reserved seat ticket...
 6.5.79: SHIPPING A warehouse supervisor is told to ship atleast 50 packages...
 6.5.80: TRUCK SCHEDULING A small company that manufacturestwo models of exe...
 6.5.81: NUTRITION A dietitian is asked to design a specialdietary supplemen...
 6.5.82: HEALTH A persons maximum heart rate iswhere is the persons age in y...
 6.5.83: DATA ANALYSIS: PRESCRIPTION DRUGS Thetable shows the retail sales (...
 6.5.84: DATA ANALYSIS: MERCHANDISE The table showsthe retail sales (in mill...
 6.5.85: PHYSICAL FITNESS FACILITY An indoor runningtrack is to be construct...
 6.5.86: TRUE OR FALSE? In Exercises 86 and 87, determinewhether the stateme...
 6.5.87: TRUE OR FALSE? In Exercises 86 and 87, determinewhether the stateme...
 6.5.88: CAPSTONE(a) Explain the difference between the graphs of theinequal...
 6.5.89: GRAPHICAL REASONING Two concentric circleshave radii and where The ...
 6.5.90: 90. The graph of the solution of the inequalityis shown in the figu...
 6.5.91: In Exercises 9194, match the system of inequalities withthe graph o...
 6.5.92: In Exercises 9194, match the system of inequalities withthe graph o...
 6.5.93: In Exercises 9194, match the system of inequalities withthe graph o...
 6.5.94: In Exercises 9194, match the system of inequalities withthe graph o...
Solutions for Chapter 6.5: Systems of Inequalities
Full solutions for College Algebra  8th Edition
ISBN: 9781439048696
Solutions for Chapter 6.5: Systems of Inequalities
Get Full SolutionsChapter 6.5: Systems of Inequalities includes 50 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: College Algebra , edition: 8. Since 50 problems in chapter 6.5: Systems of Inequalities have been answered, more than 30762 students have viewed full stepbystep solutions from this chapter. College Algebra was written by and is associated to the ISBN: 9781439048696.

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!

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).

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

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

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 .

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

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

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).

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

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

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 ().

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

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

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·