- 114.1: Tickets to the matinee are $6 each. How many tickets can Maela buyw...
- 114.2: Maria ran four laps of the track at an even pace. If it took6 minut...
- 114.3: Fifteen of the 25 members played in the game. What fraction of them...
- 114.4: Two fifths of the 160 acres were planted with alfalfa. How many acr...
- 114.5: Which digit in 94,763,581 is in the ten-thousands place?
- 114.6: a. Write two unit multipliers for these equivalent measures: 1 gall...
- 114.7: What is the sum of $36.43, $41.92, and $26.70 to the nearestdollar.
- 114.8: 4 4 in. 2 24 44
- 114.9: 314 in 212 458 4 4 in.
- 114.10: Complete the table to answer problems 1012.1 8 a. b.
- 114.11: Complete the table to answer problems 1012.a 0.9 b.
- 114.12: Complete the table to answer problems 1012.a. b. 60%
- 114.13: 3.25 23 (fraction answer)
- 114.14: Solve:3m 10 = 80
- 114.15: Solve:32 1.8m
- 114.16: Calculate mentally: a. (5)(20) b. (5)(+20)c. 205 d. 205
- 114.17: The distance between San Francisco and Los Angeles is about387 mile...
- 114.18: What is the area of this polygon?
- 114.19: What is the perimeter of this polygon?
- 114.20: Calculate mentally: a. 5 + 20 b. 20 5 c. 5 5 d. +5 20
- 114.21: Transversal t intersects parallel lines q and r. Angle 1 is halfthe...
- 114.22: Fifty people responded to the survey, a number that represented 5% ...
- 114.23: Think of two different prime numbers, and write them on your paper....
- 114.24: Write 1.5 106 as a standard number.
- 114.25: A classroom that is 30 feet long, 30 feet wide, and 10 feet high ha...
- 114.26: Convert 8 quarts to gallons using a unit multiplier.
- 114.27: A circle was drawn on a coordinate plane. The coordinates ofthe cen...
- 114.28: During one season, the highest number of points scored in one gameb...
- 114.29: 4 ft 3 in. 2 ft 9 in.
- 114.30: Study this function table anddescribe a rule for finding A when s i...
Solutions for Chapter 114: Unit Multipliers
Full solutions for Saxon Math, Course 1 | 1st Edition
Tv = Av + Vo = linear transformation plus shift.
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.
Characteristic equation det(A - AI) = O.
The n roots are the eigenvalues of A.
Column space C (A) =
space of all combinations of the columns of A.
Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A
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.
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.
Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.
Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.
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.
Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).
lA-II = 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.
Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.
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.
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)·(b - Ax) = o.
Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.
Schur complement S, D - C A -} B.
Appears in block elimination on [~ g ].
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.
Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.