- 73.1: Tomass temperature was 102F. Normal body temperatureis 98.6F. How m...
- 73.2: Jill has read 42 pages of a 180-page book. How manypages are left f...
- 73.3: If Jill wants to finish the book in the next three days, thenshe sh...
- 73.4: Write 2.5 as a reduced mixed number.
- 73.5: Write 0.35 as a reduced fraction.
- 73.6: What is the total cost of a $12.60 item when 712% (0.075) sales tax...
- 73.7: 34 2 113
- 73.8: (100 102 ) 52
- 73.9: 3 213 134
- 73.10: 516 312
- 73.11: 34 112
- 73.12: 7 0.4
- 73.13: Compare: a. 52 25 b. 0.3 0.125
- 73.14: The diameter of a quarter is about 2.4 cm. a. What is the circumfer...
- 73.15: Find each unknown number:25m = 0.175
- 73.16: Find each unknown number:1.2 + y + 4.25 = 7
- 73.17: Which digit is in the ten-thousands place in 123,456.78?
- 73.18: Arrange these numbers in order from least to greatest:1, 12, 110,14, 0
- 73.19: Write the prime factorization of 200 using exponents.
- 73.20: The store offered a 20% discount on all tools. The regular price of...
- 73.21: The length of AB is 16 mm. The length of AC is 50 mm. Whatis the le...
- 73.22: One half of the area of this square is shaded.What is the area of t...
- 73.23: Is every square a rectangle?
- 73.24: 22 232
- 73.25: The fractions chart from Lesson 72 says that the propershape for mu...
- 73.26: Refer to this coordinate plane to answer problems 26 and 27.Identif...
- 73.27: Refer to this coordinate plane to answer problems 26 and 27.Name th...
- 73.28: If s equals 9, what does s2 equal?
- 73.29: Name an every day object that has the same shape as each of thesege...
- 73.30: The measure of W inparallelogram WXYZ is 75. a. What is the measure...
Solutions for Chapter 73: Exponents Writing Decimal Numbers as Fractions, Part 2
Full solutions for Saxon Math, Course 1 | 1st Edition
Characteristic equation det(A - AI) = O.
The n roots are the eigenvalues of A.
Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).
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.
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
Dimension of vector space
dim(V) = number of vectors in any basis for V.
Eigenvalue A and eigenvector x.
Ax = AX with x#-O so det(A - AI) = o.
Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA-1 yll2 = Y T(AAT)-1 Y = 1 displayed by eigshow; axis lengths ad
Free columns of A.
Columns without pivots; these are combinations of earlier columns.
Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.
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.
Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).
Left inverse A+.
If A has full column rank n, then A+ = (AT A)-I AT has A+ A = In.
Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.
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.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.
The diagonal entry (first nonzero) at the time when a row is used in elimination.
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.
Symmetric matrix A.
The transpose is AT = A, and aU = a ji. A-I is also symmetric.
Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·