 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 153641 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: 7.

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).

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

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.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

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!).

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

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.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

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.

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.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

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

Solvable system Ax = b.
The right side b is in the column space of A.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.