 4.1.1: True or False (a) (b) (pp. A16 to A18)
 4.1.2: The solution of the inequality is __________. (pp. A24 to A25)
 4.1.3: Graph the line 2x + 3y = 6. (pp. 214)
 4.1.4: Find the point of intersection of the lines and (pp. 2226)
 4.1.5: True or False The lines are parallel. (pp. 2226)
 4.1.6: The graph of a linear inequality is called a(n) __________.
 4.1.7: True or False Sometimes the graph of a system of linear inequalitie...
 4.1.8: True or False The graph of a system of linear inequalities is somet...
 4.1.9: In 920, graph each inequality.x 0
 4.1.10: In 920, graph each inequality.y 0
 4.1.11: In 920, graph each inequality.x 6 4
 4.1.12: In 920, graph each inequality.y 6
 4.1.13: In 920, graph each inequality.y 1
 4.1.14: In 920, graph each inequality.x 7 2
 4.1.15: In 920, graph each inequality.2x + y 4
 4.1.16: In 920, graph each inequality.3x + 2y 6
 4.1.17: In 920, graph each inequality.5x + y 10
 4.1.18: In 920, graph each inequality.. x + 2y 7 4
 4.1.19: In 920, graph each inequality.x + 5y 6 5
 4.1.20: In 920, graph each inequality.3x + y 3
 4.1.21: Without graphing, determine which of the points are part of the gra...
 4.1.22: Without graphing, determine which of the points are part of the gra...
 4.1.23: Without graphing, determine which of the points are part of the gra...
 4.1.24: Without graphing, determine which of the points are part of the gra...
 4.1.25: In 2532, determine which region a, b, c, or d represents the graph ...
 4.1.26: In 2532, determine which region a, b, c, or d represents the graph ...
 4.1.27: In 2532, determine which region a, b, c, or d represents the graph ...
 4.1.28: In 2532, determine which region a, b, c, or d represents the graph ...
 4.1.29: In 2532, determine which region a, b, c, or d represents the graph ...
 4.1.30: In 2532, determine which region a, b, c, or d represents the graph ...
 4.1.31: In 2532, determine which region a, b, c, or d represents the graph ...
 4.1.32: In 2532, determine which region a, b, c, or d represents the graph ...
 4.1.33: In 3138, graph each system of inequalities.b4x  3y 124x + 3y 12
 4.1.34: In 3138, graph each system of inequalities.b6x + 3y 6x  3y 1
 4.1.35: In 3138, graph each system of inequalities.b3x + 2y 63x + 2y 0
 4.1.36: In 3138, graph each system of inequalities.b x  2y 42x  4y 0
 4.1.37: In 3138, graph each system of inequalities.b 5x  2y 1010x  4y 0
 4.1.38: In 3138, graph each system of inequalities.bx + y 1x + y 2
 4.1.39: In 3950, (a) graph each system of linear inequalities and (b) deter...
 4.1.40: In 3950, (a) graph each system of linear inequalities and (b) deter...
 4.1.41: In 3950, (a) graph each system of linear inequalities and (b) deter...
 4.1.42: In 3950, (a) graph each system of linear inequalities and (b) deter...
 4.1.43: In 3950, (a) graph each system of linear inequalities and (b) deter...
 4.1.44: In 3950, (a) graph each system of linear inequalities and (b) deter...
 4.1.45: In 3950, (a) graph each system of linear inequalities and (b) deter...
 4.1.46: In 3950, (a) graph each system of linear inequalities and (b) deter...
 4.1.47: In 3950, (a) graph each system of linear inequalities and (b) deter...
 4.1.48: In 3950, (a) graph each system of linear inequalities and (b) deter...
 4.1.49: In 3950, (a) graph each system of linear inequalities and (b) deter...
 4.1.50: In 3950, (a) graph each system of linear inequalities and (b) deter...
 4.1.51: Mixture Nuts has 60 pounds of almonds and 90 pounds of peanuts avai...
 4.1.52: Mixture Nuts has 60 pounds of cashews and 90 pounds of peanuts avai...
 4.1.53: Manufacturing Mikes Famous Toy Trucks company manufactures two kind...
 4.1.54: Manufacturing Repeat if the company only has one grinder and two fi...
 4.1.55: Financial Planning The Harpers have up to $25,000 to invest. As the...
 4.1.56: Financial Planning Use the information supplied in 55, along with t...
 4.1.57: Nutrition A farmer prepares feed for livestock by combining two typ...
 4.1.58: . Investment Strategy Kathleen wishes to invest up to a total of $4...
 4.1.59: Nutrition To maintain an adequate daily diet, nutritionists recomme...
 4.1.60: Transportation A microwave company has two plants, one on the East ...
 4.1.61: . Financial Planning In March 2010, a couple plans to invest $30,00...
 4.1.62: Financial Planning The members of an investment club decide to depo...
 4.1.63: . Mutual Funds The table lists two mutual funds: the John Hancock L...
 4.1.64: Home Mortgages On March 1, 2010, Fremont Bank offered noclosingco...
 4.1.65: Make up a system of linear inequalities that has no solution.
 4.1.66: Make up a system of linear inequalities that has a single point as ...
 4.1.67: Draw a graph that is unbounded. How would you convince someone that...
Solutions for Chapter 4.1: Systems of Linear Inequalities
Full solutions for Finite Mathematics, Binder Ready Version: An Applied Approach  11th Edition
ISBN: 9780470876398
Solutions for Chapter 4.1: Systems of Linear Inequalities
Get Full SolutionsSince 67 problems in chapter 4.1: Systems of Linear Inequalities have been answered, more than 16903 students have viewed full stepbystep solutions from this chapter. Chapter 4.1: Systems of Linear Inequalities includes 67 full stepbystep solutions. This textbook survival guide was created for the textbook: Finite Mathematics, Binder Ready Version: An Applied Approach, edition: 11. This expansive textbook survival guide covers the following chapters and their solutions. Finite Mathematics, Binder Ready Version: An Applied Approach was written by and is associated to the ISBN: 9780470876398.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

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

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

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

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

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.

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.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

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

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.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

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).

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

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

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

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·