 2.1: If 2x 1 =5, then x = 3.
 2.2: If she's smart, then I'm a genius.
 2.3: 8v = 40 implies y = 5.
 2.4: RS = jRT if S is the midpoint of RT.
 2.5: ^\ = ^2 if mA\ = msL2.
 2.6: Zl = Z2 only if m L 1 = m L 2.
 2.7: Combine the conditionals in Exercises 5 and 6 into a single bicondi...
 2.8: 8. If AB = BC, then B is the midpoint of AC.
 2.9: If a line lies in a vertical plane, then the line is vertical.
 2.10: If a number is divisible by 4, then it is divisible by 6.
 2.11: If a number is divisible by 4, then it is divisible by 6.11. If x2 ...
 2.12: If today is Friday, then tomorrow is Saturday.
 2.13: If x > 0, then x~ > 0.
 2.14: If a number is divisible by 6, then it is divisible by 3.
 2.15: If 6x = 18, then x = 3.
 2.16: Give an example of a false conditional whose converse is true
 2.17: Tell whether each statement is true or false. Then write the conver...
 2.18: Tell whether each statement is true or false. Then write the conver...
 2.19: Tell whether each statement is true or false. Then write the conver...
 2.20: Tell whether each statement is true or false. Then write the conver...
 2.21: Tell whether each statement is true or false. Then write the conver...
 2.22: Tell whether each statement is true or false. Then write the conver...
 2.23: Tell whether each statement is true or false. Then write the conver...
 2.24: Tell whether each statement is true or false. Then write the conver...
 2.25: Tell whether each statement is true or false. Then write the conver...
 2.26: Tell whether each statement is true or false. Then write the conver...
 2.27: Tell whether each statement is true or false. Then write the conver...
 2.28: Tell whether each statement is true or false. Then write the conver...
 2.29: Tell whether each statement is true or false. Then write the conver...
 2.30: Tell whether each statement is true or false. Then write the conver...
 2.31: Tell whether each statement is true or false. Then write the conver...
 2.32: Find the values of x and v for each diagram.
 2.33: Find the values of x and v for each diagram.
 2.34: Can the measure of a complement of an angle ever equal exactly half...
 2.35: You are told that the measure of an acute angle is equal to the dif...
Solutions for Chapter 2: IfThen Statements; Converses
Full solutions for Geometry  1st Edition
ISBN: 9780395977279
Solutions for Chapter 2: IfThen Statements; Converses
Get Full SolutionsThis textbook survival guide was created for the textbook: Geometry, edition: 1. Since 35 problems in chapter 2: IfThen Statements; Converses have been answered, more than 5757 students have viewed full stepbystep solutions from this chapter. Geometry was written by and is associated to the ISBN: 9780395977279. Chapter 2: IfThen Statements; Converses includes 35 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

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

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

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.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

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.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

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

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

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)ยท(b  Ax) = o.

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.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

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

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.