- 102.1: On his first six tests, Chris had scores of 90%, 92%, 96%, 92%, 84%...
- 102.2: On his first six tests, Chris had scores of 90%, 92%, 96%, 92%, 84%...
- 102.3: In basketball there are one-point baskets, two-point baskets, andth...
- 102.4: Which ratio forms a proportion with 47?A 74 B 1417 C 1221 D 23
- 102.5: Complete this proportion: Four is to five as what number is totwenty?
- 102.6: Arrange these numbers in order from least to greatest:1, 1, 0.1, 0....
- 102.7: The product of 103 102 equals which of the following? A 109 B 106 C...
- 102.8: The area of the square in this figure is100 mm2. a. What is the rad...
- 102.9: Complete the table to answer problems 911.425 a. b.
- 102.10: Complete the table to answer problems 911.a. 0.01 b.
- 102.11: Complete the table to answer problems 911.a. b. 90%
- 102.12: 1 23 312 416
- 102.13: 56 310 x 4
- 102.14: 614 100
- 102.15: 6.437 + 12.8 + 7
- 102.16: Conver 17 to a decimal number by dividing 1 by 7. Stopdividing afte...
- 102.17: An octagon has how many more sides than a pentagon?
- 102.18: 4 52 50 24 (32 23)
- 102.19: Sector 2 on this spinner is a 90sector. If the spinner is spun twic...
- 102.20: If the spinner is spun 100 times, about how many times would it bee...
- 102.21: How many 1 inch cubes would be needed tobuild this larger cube?
- 102.22: The average of four numbers is 5. What is their sum?
- 102.23: When Andy was born, he weighed 8 pounds 4 ounces. Threeweeks later ...
- 102.24: Lines s and t are parallel. a. Which angle is an alternate interior...
- 102.25: Find the missing number in this function table:
- 102.26: What is the perimeter of this hexagon?Dimensions are in centimeters.
- 102.27: a. What is the area of the parallelogram atright? b. What is the ar...
- 102.28: How many milligrams is half of a gram?
- 102.29: The coordinates of the endpoints of a line segment are (3, 1)and (3...
- 102.30: Tania took 10 steps to walk across the tetherball circle and31 step...
Solutions for Chapter 102: Mass and Weight
Full solutions for Saxon Math, Course 1 | 1st Edition
Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or - sign.
Column space C (A) =
space of all combinations of the columns of A.
cond(A) = c(A) = IIAIlIIA-III = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.
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).
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].
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!).
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.
Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.
Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , Aj-Ib. Numerical methods approximate A -I b by x j with residual b - Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.
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.
Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A - AI) if no eigenvalues are repeated; always meA) divides peA).
A directed graph that has constants Cl, ... , Cm associated with the edges.
Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or -1) based on the number of row exchanges to reach I.
Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.
Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.
Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.
Similar matrices A and B.
Every B = M-I AM has the same eigenvalues as A.
Solvable system Ax = b.
The right side b is in the column space of A.
Constant down each diagonal = time-invariant (shift-invariant) filter.