 6.1: Classify each conditional as true or false. If 3a > 9. then a > 27.
 6.2: Classify each conditional as true or false. If 4ft > 20. then ft > 5.
 6.3: Classify each conditional as true or false. If x > 4. then x + 1 > 5.
 6.4: Classify each conditional as true or false. If x + 1 > 5, then .v > 4.
 6.5: Classify each conditional as true or false. If c  5 > 45. then c >...
 6.6: Classify each conditional as true or false. If a + ft = n and c > f...
 6.7: Classify each conditional as true or false. If v > 18. then v > 20.
 6.8: Classify each conditional as true or false. If v > 20. then y > 18.
 6.9: Classify each conditional as true or false. If a > 5 and 5 > ft. th...
 6.10: Classify each conditional as true or false. If d > e and f>e, then ...
 6.11: Classify each conditional as true or false. If g > h and / = ft. th...
 6.12: Classify each conditional as true or false. If p = q + 6. then p > q.
 6.13: Classify each conditional as true or false. If c > d and ? = /. the...
 6.14: Classify each conditional as true or false. If g > h and /' > /. th...
 6.15: Classify each conditional as true or false. If A > / and m > //. t...
 6.16: Classify each conditional as true or false. If a > ft. then 100  a...
 6.17: a. XZb. XZc. XZXYXYYZYZ
 6.18: a. m Z. 1b. mZ2c. m Z 1mZ.3mZ3wZ2
 6.19: a. Afi _L_ ACb. Afi _Z_ AX + XBc. Afi _!_ XBd. AC _L_ XB
 6.20: Supply reasons to complete the proof.Given: mZ.2 > m Z 1Prove: m Z....
 6.21: Urn LA + mLB 180,then mLD + m LC 180.
 6.22: If n1is not a multiple of 3.then n is not a multiple of 3.
 6.23: Discover, state, and prove a theorem that compares the length of th...
 6.24: Prove: If P is any point inside AXYZ. then ZX + ZY > PX + PY.
Solutions for Chapter 6: Inequalities
Full solutions for Geometry  1st Edition
ISBN: 9780395977279
Solutions for Chapter 6: Inequalities
Get Full SolutionsGeometry was written by and is associated to the ISBN: 9780395977279. Since 24 problems in chapter 6: Inequalities have been answered, more than 5249 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Geometry, edition: 1. Chapter 6: Inequalities includes 24 full stepbystep solutions.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

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.)

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

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

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 .

Iterative method.
A sequence of steps intended to approach the desired solution.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

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

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

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

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

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

Solvable system Ax = b.
The right side b is in the column space of A.

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

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

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