 21.1: Vocabulary Explain why a conjecture may be true or false.
 21.2: Find the next item in each pattern.March, May, July,
 21.3: Find the next item in each pattern.13 , _24 , _35 ,
 21.4: Find the next item in each pattern.4
 21.5: Complete each conjectureThe product of two even numbers is ? .
 21.6: Complete each conjectureA rule in terms of n for the sum of the fir...
 21.7: Biology A laboratory culture contains 150 bacteria. After twenty mi...
 21.8: Show that each conjecture is false by finding acounterexample.Kenne...
 21.9: Show that each conjecture is false by finding acounterexample.Three...
 21.10: Show that each conjecture is false by finding acounterexample.For a...
 21.11: Find the next item in each pattern.8 A.M., 11 A.M., 2 P.M.,
 21.12: Find the next item in each pattern.75, 64, 53,
 21.13: Find the next item in each pattern.13
 21.14: Complete each conjecture. A rule in terms of n for the sum of the f...
 21.15: Complete each conjecture. The number of nonoverlapping segments for...
 21.16: Industrial Arts About 5% of the students at Lincoln High School usu...
 21.17: Show that each conjecture is false by finding a counterexample.If 1...
 21.18: Show that each conjecture is false by finding a counterexample.For ...
 21.19: Show that each conjecture is false by finding a counterexample.Ever...
 21.20: Make a conjecture about each pattern. Write the next two items.2, 4...
 21.21: Make a conjecture about each pattern. Write the next two items.12 ,...
 21.22: Make a conjecture about each pattern. Write the next two items.3, 6...
 21.23: Draw a square of dots. Make a conjecture about thenumber of dots ne...
 21.24: Determine if each conjecture is true. If not, write or draw a count...
 21.25: Determine if each conjecture is true. If not, write or draw a count...
 21.26: Determine if each conjecture is true. If not, write or draw a count...
 21.27: Determine if each conjecture is true. If not, write or draw a count...
 21.28: Estimation The Westside High School band is selling coupon books to...
 21.29: Write each fraction in the pattern _111 , _211 , _311 , as a repeat...
 21.30: Math History Remember that a prime number is a whole number greater...
 21.31: The pattern 1, 1, 2, 3, 5, 8, 13, 21, is known as the Fibonacci seq...
 21.32: Look at a monthly calendar and pick any three squares in a rowacros...
 21.33: Make a conjecture about the value of 2n  1when n is an integer.
 21.34: Critical Thinking The turnaround date for migrating gray whales occ...
 21.35: Write About It Explain why a true conjecture about even numbers doe...
 21.36: This problem will prepare you forthe Concept Connection on page 102...
 21.37: Which of the following conjectures is false? If x is odd, then x + ...
 21.38: A student conjectures that if x is a prime number, then x + 1 is no...
 21.39: The class of 2004 holds a reunion each year. In 2005, 87.5% of the ...
 21.40: MultiStep Make a table of values for the rule x 2 + x + 11 when x ...
 21.41: Political Science Presidential elections are held every four years....
 21.42: Physical Fitness Rob is training for the Presidents Challenge physi...
 21.43: Construction Draw AB . Then construct point C so that it is not on ...
 21.44: Determine if the given point is a solution to y = 3x  5. (Previous...
 21.45: Determine if the given point is a solution to y = 3x  5. (Previous...
 21.46: Determine if the given point is a solution to y = 3x  5. (Previous...
 21.47: Determine if the given point is a solution to y = 3x  5. (Previous...
 21.48: Find the perimeter or circumference of each of the following. Leave...
 21.49: Find the perimeter or circumference of each of the following. Leave...
 21.50: Find the perimeter or circumference of each of the following. Leave...
 21.51: Find the perimeter or circumference of each of the following. Leave...
 21.52: A triangle has vertices (1, 1) , (0, 1) , and (4, 0) . Find the c...
 21.53: A triangle has vertices (1, 1) , (0, 1) , and (4, 0) . Find the c...
Solutions for Chapter 21: Using Inductive Reasoning to Make Conjectures
Full solutions for Geometry  1st Edition
ISBN: 9780030923456
Solutions for Chapter 21: Using Inductive Reasoning to Make Conjectures
Get Full SolutionsGeometry was written by and is associated to the ISBN: 9780030923456. Chapter 21: Using Inductive Reasoning to Make Conjectures includes 53 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Geometry, edition: 1. Since 53 problems in chapter 21: Using Inductive Reasoning to Make Conjectures have been answered, more than 47149 students have viewed full stepbystep solutions from this chapter.

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).

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

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

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

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

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

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

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).

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

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.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

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

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

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.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B IIĀ·

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.