 4.5.1E: Which memory locations are assigned by the hashing function h (k) =...
 4.5.2E: Which memory locations are assigned by the hashing function h (k) =...
 4.5.3E: A parking lot has 31 visitor spaces, numbered from 0 to 30. Visitor...
 4.5.4E: Use the double hashing procedure we have described with p = 4969 to...
 4.5.5E: What sequence of pseudorandom numbers is generated using the linear...
 4.5.6E: What sequence of pseudorandom numbers is generated using the linear...
 4.5.7E: What sequence of pseudorandom numbers is generated using the pure m...
 4.5.8E: Write an algorithm in pseudocode for generating a sequence of pseud...
 4.5.9E: Find the first eight terms of the sequence of fourdigit pseudorand...
 4.5.10E: Explain why both 3792 and 2916 would be bad choices for the initial...
 4.5.11E: Find the sequence of pseudorandom numbers generated by the power ge...
 4.5.12E: Find the sequence of pseudorandom numbers generated by the power ge...
 4.5.13E: Suppose you received these bit strings over a communications link, ...
 4.5.14E: Prove that a parity check bit can detect an error in a string if an...
 4.5.15E: The first nine digits of the ISBN10 of the European version of the...
 4.5.16E: The ISBN10 of the sixth edition of Elementary Number Theory and It...
 4.5.17E: Determine whether the check digit of the ISBN10 for this textbook ...
 4.5.18E: Find the check digit for the USPS money orders that have identifica...
 4.5.19E: Determine whether each of these numbers is a valid USPS money order...
 4.5.20E: One digit in each of these identification numbers of a postal money...
 4.5.21E: One digit in each of these identification numbers of a postal money...
 4.5.22E: Determine which single digit errors are detected by the USPS money ...
 4.5.23E: Determine which transposition errors are detected by the USPS money...
 4.5.24E: Determine the check digit for the UPCs that have these initial 11 d...
 4.5.25E: Determine whether each of the strings of 12 digits is a valid UPC c...
 4.5.26E: Does the check digit of a UPC code detect all single errors? Prove ...
 4.5.27E: Determine which transposition errors the check digit of a UPC code ...
 4.5.28E: Find the check digit a15 that follows each of these initial 14 digi...
 4.5.29E: Determine whether each of these 15digit numbers is a valid airline...
 4.5.30E: Which errors in a single digit of a 15digit airline ticket identif...
 4.5.31E: Can the accidental transposition of two consecutive digits in an ai...
 4.5.32E: For each of these initial seven digits of an ISSN, determine the ch...
 4.5.33E: Are each of these eightdigit codes possible ISSNs? That is, do the...
 4.5.34E: Does the check digit of an ISSN detect every single error in an ISS...
 4.5.35E: Does the check digit of an ISSN detect every error where two consec...
Solutions for Chapter 4.5: Discrete Mathematics and Its Applications 7th Edition
Full solutions for Discrete Mathematics and Its Applications  7th Edition
ISBN: 9780073383095
Solutions for Chapter 4.5
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 35 problems in chapter 4.5 have been answered, more than 91201 students have viewed full stepbystep solutions from this chapter. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. Chapter 4.5 includes 35 full stepbystep solutions. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7th.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

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.

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

Column space C (A) =
space of all combinations of the columns of A.

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.

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

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

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.

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).

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).

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

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

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

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

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.