 39.1: Mount Everest, the worlds tallest mountain, rises to an elevation o...
 39.2: There are three feet in a yard. About how many yards above sea leve...
 39.3: If you had lived in the 1800s, you may have seen a sign likethis in...
 39.4: 0.25 0.5
 39.5: $1.80 10
 39.6: 63 0.7
 39.7: 1.23 1.23 + 216 0.5
 39.8: 12.34 5.6
 39.9: (1.1)2
 39.10: Write ten and three tenths a. as a decimal number. b. as a mixed nu...
 39.11: Think of two different fractions that are greater than zerobut less...
 39.12: Write the decimal number one hundred twentythreethousandths.
 39.13: Write (6 100) + (4 10) in standard form.
 39.14: The perimeter of a square is 40 inches. How many squaretiles with s...
 39.15: What is the least common multiple (LCM) of 2, 3, and 6?
 39.16: Convert 208 to a mixed number. Simplify your answer. Remember tored...
 39.17: a13 23b 1
 39.18: 35 23
 39.19: 89 98
 39.20: A pie was cut into six equal slices. Two slices were eaten.What fra...
 39.21: What time is 2 12 hours before 1 a.m.?
 39.22: On Hiroshis last four assignments he had 26, 29, 28, and 25 correct...
 39.23: Estimate the quotient of 7987 divided by 39.
 39.24: Compare: 365 364 364 365
 39.25: Which digit in 3.675 has the same place value as the 4 in 14.28?
 39.26: Use an inch ruler to find the length of the segment below tothe nea...
 39.27: a. How many 35 s are in 1? b. Use the answer to part a to find the ...
 39.28: Instead of solving the division problem 390 15, Rooseveltdivided bo...
 39.29: Find the area of the rectangle below.
 39.30: In the figure below, what is the ratio of the measure of ABCto the ...
Solutions for Chapter 39: Multiplying Decimal Numbers
Full solutions for Saxon Math, Course 1  1st Edition
ISBN: 9781591417835
Solutions for Chapter 39: Multiplying Decimal Numbers
Get Full SolutionsSince 30 problems in chapter 39: Multiplying Decimal Numbers have been answered, more than 35629 students have viewed full stepbystep solutions from this chapter. Chapter 39: Multiplying Decimal Numbers includes 30 full stepbystep solutions. This textbook survival guide was created for the textbook: Saxon Math, Course 1, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Saxon Math, Course 1 was written by and is associated to the ISBN: 9781591417835.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

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!).

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

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.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

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.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).