 6.4.1: Write each number in scientific notation. a. 34,000,000,000 b. 2,10...
 6.4.2: Write each number in standard notation. a. 7.4 104 b. 2.134 106 c. ...
 6.4.3: Use the properties of exponents to rewrite each expression. a. 3x5(...
 6.4.4: Use the properties of exponents to rewrite each expression. a. 3x2 ...
 6.4.5: Owen insists on reading his calculators display as three point five...
 6.4.6: There are approximately 5.58 1021 atoms in a gram of silver. How ma...
 6.4.7: Because the number of molecules in a given amount of a compound is ...
 6.4.8: Write each number in scientific notation. How does your calculator ...
 6.4.9: Cal and Al were assigned this multiplication problem for homework: ...
 6.4.10: Consider these multiplication expressions: i. (2 105)(3 108) ii. (6...
 6.4.11: . Americans make almost 2 billion telephone calls each day. (www.br...
 6.4.12: On average a person sheds 1 million dead skin cells every 40 minute...
 6.4.13: A lightyear is the distance light can travel in one year. This dis...
 6.4.14: APPLICATION The exponential equation P = 3.8(1 + 0.017)t approximat...
 6.4.15: Graph y 2(x 5).
Solutions for Chapter 6.4: Scientific Notation for Large Numbers
Full solutions for Discovering Algebra: An Investigative Approach  2nd Edition
ISBN: 9781559537636
Solutions for Chapter 6.4: Scientific Notation for Large Numbers
Get Full SolutionsThis textbook survival guide was created for the textbook: Discovering Algebra: An Investigative Approach, edition: 2. This expansive textbook survival guide covers the following chapters and their solutions. Discovering Algebra: An Investigative Approach was written by and is associated to the ISBN: 9781559537636. Chapter 6.4: Scientific Notation for Large Numbers includes 15 full stepbystep solutions. Since 15 problems in chapter 6.4: Scientific Notation for Large Numbers have been answered, more than 5931 students have viewed full stepbystep solutions from this chapter.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

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

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

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).

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.

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 IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Iterative method.
A sequence of steps intended to approach the desired solution.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

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.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

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.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

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