- 3-1.1: Write the word name for the decimal. 0.582
- 3-1.2: Write the word name for the decimal. 0.21
- 3-1.3: Write the word name for the decimal. 1.0009
- 3-1.4: Write the word name for the decimal. 2.83
- 3-1.5: Write the word name for the decimal. 782.07
- 3-1.6: Write the number that represents the decimal. Thirty-five hundredths
- 3-1.7: Write the number that represents the decimal. Three hundred twelve ...
- 3-1.8: Write the number that represents the decimal. Sixty and twenty-eigh...
- 3-1.9: Write the number that represents the decimal. Five and three hundre...
- 3-1.10: Round to the nearest dollar $493.91
- 3-1.11: Round to the nearest dollar $785.03
- 3-1.12: Round to the nearest dollar $19.80
- 3-1.13: Round to the nearest cent $0.5239
- 3-1.14: Round to the nearest cent $21.09734
- 3-1.15: Round to the nearest cent $32,048.87219
- 3-1.16: Round to the nearest tenth. 42.3784
- 3-1.17: Round to the nearest tenth. 17.03752
- 3-1.18: Round to the nearest tenth. 4.293
- 3-1.19: Tel-Sales, Inc., a prepaid phone card company in Oklahoma City, sel...
- 3-1.20: Destiny Telecom of Oakland, California, introduced a Braille prepai...
- 3-1.21: GameStop reported a quarterly gross margin of 839.18 dollars in mil...
- 3-1.22: Gannett Company reported a quarterly income before tax of negative ...
Solutions for Chapter 3-1: DECIMALS AND THE PLACE-VALUE SYSTEM
Full solutions for Business Math, | 9th Edition
peA) = det(A - AI) has peA) = zero matrix.
Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).
Eigenvalue A and eigenvector x.
Ax = AX with x#-O so det(A - AI) = o.
Free variable Xi.
Column i has no pivot in elimination. We can give the n - r free variables any values, then Ax = b determines the r pivot variables (if solvable!).
Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.
A sequence of steps intended to approach the desired solution.
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.
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.
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).
If N NT = NT N, then N has orthonormal (complex) eigenvectors.
The diagonal entry (first nonzero) at the time when a row is used in elimination.
Reflection matrix (Householder) Q = I -2uuT.
Unit vector u is reflected to Qu = -u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q-1 = Q.
Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.
Singular matrix A.
A square matrix that has no inverse: det(A) = o.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!
Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).
Symmetric matrix A.
The transpose is AT = A, and aU = a ji. A-I is also symmetric.
Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.
Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.