 10.1: In 16, determine whether the Markov chain whose transition matrix P...
 10.2: In 16, determine whether the Markov chain whose transition matrix P...
 10.3: In 16, determine whether the Markov chain whose transition matrix P...
 10.4: In 16, determine whether the Markov chain whose transition matrix P...
 10.5: In 16, determine whether the Markov chain whose transition matrix P...
 10.6: In 16, determine whether the Markov chain whose transition matrix P...
 10.7: In 710, find the fixed probability vector t of each regular Markov ...
 10.8: In 710, find the fixed probability vector t of each regular Markov ...
 10.9: In 710, find the fixed probability vector t of each regular Markov ...
 10.10: In 710, find the fixed probability vector t of each regular Markov ...
 10.11: .7 0.1 0.2 0.6 0.1 0.3 0.4 0.2 0.4 P = F S
 10.12: 0.3 0.5 0.2 0.1 0.6 0.3 0.9 0 0.1 P = C S
 10.13: . Customer Loyalty Three beer distributors, A, B, and C, each prese...
 10.14: If the current share of the market for each distributor A, B, and C...
 10.15: In 1522, use the transition matrices P of the following Markov chai...
 10.16: In 1522, use the transition matrices P of the following Markov chai...
 10.17: In 1522, use the transition matrices P of the following Markov chai...
 10.18: In 1522, use the transition matrices P of the following Markov chai...
 10.19: In 1522, use the transition matrices P of the following Markov chai...
 10.20: In 1522, use the transition matrices P of the following Markov chai...
 10.21: In 1522, use the transition matrices P of the following Markov chai...
 10.22: In 1522, use the transition matrices P of the following Markov chai...
 10.23: Gamblers Ruin a man has $2, which he is going to bet $1 at a time u...
 10.24: Gamblers Ruin Suppose a man has $10, and he will bet $5 at a time u...
 10.25: In 2530, determine which of the twoperson zerosum games are stric...
 10.26: In 2530, determine which of the twoperson zerosum games are stric...
 10.27: In 2530, determine which of the twoperson zerosum games are stric...
 10.28: In 2530, determine which of the twoperson zerosum games are stric...
 10.29: In 2530, determine which of the twoperson zerosum games are stric...
 10.30: In 2530, determine which of the twoperson zerosum games are stric...
 10.31: Find the expected payoff of the game for the strategies
 10.32: Find the expected payoff of the game for the strategies
 10.33: Find the expected payoff of the game for the strategies
 10.34: Find the expected payoff of the game for the strategies
 10.35: Find the expected payoff of the game for the strategies
 10.36: Find the expected payoff of the game for the strategies
 10.37: Find the optimal strategy for the game described in 31.
 10.38: . Find the optimal strategy for the game described in 33.
 10.39: Investment Strategy An investor has a choice of two investments, A ...
 10.40: Investment Strategy There are two possible investments, A and B, an...
 10.41: Real Estate Development A real estate developer has bought a large ...
 10.42: Betting Strategy The Pistons are going to play the Bulls in a baske...
Solutions for Chapter 10: Markov Chains; Games
Full solutions for Finite Mathematics, Binder Ready Version: An Applied Approach  11th Edition
ISBN: 9780470876398
Solutions for Chapter 10: Markov Chains; Games
Get Full SolutionsThis textbook survival guide was created for the textbook: Finite Mathematics, Binder Ready Version: An Applied Approach, edition: 11. Since 42 problems in chapter 10: Markov Chains; Games have been answered, more than 15997 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Finite Mathematics, Binder Ready Version: An Applied Approach was written by and is associated to the ISBN: 9780470876398. Chapter 10: Markov Chains; Games includes 42 full stepbystep solutions.

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

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.

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

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

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

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

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).

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).

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

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.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

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

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

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

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.