- 17.1: What is the sum of twelve thousand, five hundred and ten thousand,s...
- 17.2: In 1903 the Wright brothers made the first powered airplane flight....
- 17.3: Linda can run about 6 yards in one second. About how far can she ru...
- 17.4: A coin collector has a collection of two dozen rare coins. If the v...
- 17.5: Find the sum of 5280 and 1760 by rounding each number tothe nearest...
- 17.6: 4803
- 17.7: 6 63
- 17.8: The letters a, b, and c represent three different numbers.The sum o...
- 17.9: Rewrite 2 3 with a division bar, but do not divide.
- 17.10: A square has sides 10 cm long. Describe how to find its perimeter.
- 17.11: Use a ruler to find the length of the line segment below to thenear...
- 17.12: Find each unknown number. Check your work$3 y = $1.75
- 17.13: Find each unknown number. Check your workm 20 = 30
- 17.14: Find each unknown number. Check your work12n = 0
- 17.15: Find each unknown number. Check your work16 + 14 = 14 + w
- 17.16: Find each unknown number. Check your workCompare: 19 21 20 20
- 17.17: Find each unknown number. Check your work100 (50 25)
- 17.18: Find each unknown number. Check your work528044
- 17.19: Find each unknown number. Check your work365 + 4576 + 50,287
- 17.20: What number is missing in the following sequence?5, 10, , 20, 25,
- 17.21: Which digit in 987,654,321 is in the hundred-millions place?
- 17.22: 250,000 100
- 17.23: $3.75 10
- 17.24: An 8-ounce serving of 2% milk contains 26 grams of protein,fat, and...
- 17.25: What is the sum of the first six positive odd numbers?
- 17.26: How can you find 14 of 52?
- 17.27: A quarter is 14 of a dollar. a. How many quarters are in one dollar...
- 17.28: On an inch ruler, which mark is halfway between the 14-inch mark an...
- 17.29: Point A represents what mixed number on the number line below?
- 17.30: A segment that is 12 of an inch long is how many sixteenths of an i...
Solutions for Chapter 17: The Number Line: Fractions and Mixed Numbers
Full solutions for Saxon Math, Course 1 | 1st Edition
Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.
Characteristic equation det(A - AI) = O.
The n roots are the eigenvalues of A.
Put CI, ... ,Cn in row n and put n - 1 ones just above the main diagonal. Then det(A - AI) = ±(CI + c2A + C3A 2 + .•. + cnA n-l - An).
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
Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.
0,1,1,2,3,5, ... satisfy Fn = Fn-l + Fn- 2 = (A7 -A~)I()q -A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].
Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.
Incidence matrix of a directed graph.
The m by n edge-node incidence matrix has a row for each edge (node i to node j), with entries -1 and 1 in columns i and j .
A sequence of steps intended to approach the desired solution.
The diagonal entry (first nonzero) at the time when a row is used in elimination.
Rank r (A)
= number of pivots = dimension of column space = dimension of row space.
Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).
Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.
R = [~ CS ] rotates the plane by () and R- 1 = RT rotates back by -(). Eigenvalues are eiO and e-iO , eigenvectors are (1, ±i). c, s = cos (), sin ().
Row space C (AT) = all combinations of rows of A.
Column vectors by convention.
Singular matrix A.
A square matrix that has no inverse: det(A) = o.
Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.
Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.
Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.