 151.1: What was the closing price in dollars and cents?
 151.2: During the previous year, what was its high price? Its low price?
 151.3: What is the difference between this days high price and low price?
 151.4: What was the previous days closing price?
 151.5: How many shares of AK Steel stock were sold?
 151.6: AFL stock had what P/E ratio?
 151.7: Find the current yield of American Water Works Co. that reported a ...
 151.8: Find the current yield of Baxter International, Inc., that reported...
 151.9: Find the P/E ratio of a corporation that reported last years net in...
 151.10: Find the P/E ratio of Amcol International Corp. that reported last ...
 151.11: If AFL (Table 151) had 989,532,000 shares of common stock outstand...
 151.12: What was the market value of AFLs stock that was traded on this day...
 151.13: How much money goes to preferred stockholders?
 151.14: How much money goes to common stockholders?
 151.15: How much per share does a common stockholder receive in dividends t...
 151.16: How much money goes to preferred stockholders?
 151.17: How much money goes to common stockholders?
 151.18: How much per share does a common stockholder receive in dividends t...
Solutions for Chapter 151: STOCKS
Full solutions for Business Math,  9th Edition
ISBN: 9780135108178
Solutions for Chapter 151: STOCKS
Get Full SolutionsSince 18 problems in chapter 151: STOCKS have been answered, more than 17969 students have viewed full stepbystep solutions from this chapter. Business Math, was written by and is associated to the ISBN: 9780135108178. Chapter 151: STOCKS includes 18 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Business Math, , edition: 9.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

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

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Fundamental Theorem.
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.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

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.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

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

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.