18 Pages

cs411-s04-hw3

Course: CS 511, Fall 2008
School: University of Illinois,...
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Word Count: 15448

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Coursehero >> Illinois >> University of Illinois, Urbana Champaign >> CS 511

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University of Illinois, Urbana Champaign - CS - 511
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University of Illinois, Urbana Champaign - CS - 511
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University of Illinois, Urbana Champaign - CS - 591
UT-AustinThe Department Created in 1966 42 tenure-track faculty 190 PhD students, 50 master students, 1300 undergraduate students. Chair: Jayadev Misra Edsger Dijkstra (chair from 1984 to 1997)Research Areastop-10 CS program Formal Methods
University of Illinois, Urbana Champaign - CS - 591
University of Southern California (USC)A Review of Database Related Research GroupsSeptember 2005Compuer Science Department History: Established in 1972 People (as of 2004): Tenure Track Faculty: 27 Joint Faculty: 18 Research Faculty:
University of Illinois, Urbana Champaign - CS - 591
Cornell UniversityDavid Killian 10/25/2005Cornell Tidbits Founded 1865 2,627 Faculty 13,625 Undergraduates, 5,903 Graduates Colors: Carnelian and white Mascot: &quot;Big Red Bear&quot; Yougest Ivy League, largest Ivy League (enrollment) First major
Columbus State University - MATH - 1127
Chapter 1 - Additional Practice ProblemsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Classify the study as either descriptive or inferential. 1) The table below shows the number of new AIDS
Columbus State University - MATH - 1127
Chapter 2 - Practice ProblemsSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Explain the difference between a frequency distribution and a relative frequency dis
Columbus State University - MATH - 1127
Chapter 2 - Additional Practice ProblemsSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Construct a grouped-data table for the given data. 1) Kevin asked some of his friends how many hours they had
Columbus State University - MATH - 1127
Chapter 3 - Additional Practice ProblemsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decima
Columbus State University - MATH - 1127
Chapter 4 - Practice ProblemsSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Compare the relative frequency formula for finding probabilities to the classical fo
Columbus State University - MATH - 1127
Chapter 5 - Additional Practice Problems Binomial Distribution MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. 12 1) 2 A) 66 20 1 A) 19 B) 21 C) 1 D) 20 B) 3,628,800 C) 7
Columbus State University - MATH - 1127
Chapter 8 - Practice ProblemsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A hypothesis test is to be performed. Determine the null and alternative hypotheses. 1) In the past, the mean running
Columbus State University - MATH - 1127
Chapter 10 - Additional Practice ProblemsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the regression equation for the data. Round the final values to three significant digits, if ne
Columbus State University - MATH - 1131
Sample Final ExamProblem 1) The graph of f ( x) is given below. Estimate the following values. (1 point each)8y 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 x 6a) lim+ f ( x ) =x -6b) lim- f ( x ) =x -3c) lim+ f ( x ) =x -3d) lim- f ( x
Columbus State University - MATH - 2115
Introduction to linear AlgebraIntroduction and OverviewLinear algebra is a number of things, including: an area of mathematical study that is accessible to students who have completed at least one semester of calculus, an introduction to some of
Columbus State University - MATH - 2115
Section 1.2 - Row Reduction and Echelon FormsRow Reduction and Echelon Forms In this section we refine the method of section1.1 into a row reduction algorithm that will enable us to analyze any linear system. By using the first part of the algor
Columbus State University - MATH - 2115
Section 1.3 Vector EquationsVectors in an A matrix with only one column is called acolumn vector or simply a vector. Vectors will be denoted, in general, by lower caserLatin r r letters with an arrow on top such as a , u , v ,K Examples: 3
Columbus State University - MATH - 2115
Section 1.4 r r The Matrix Equation Ax = bMain Idea The fundamental idea of this section is to viewlinear combination of vectors as the product of a matrix and a vector.Definitionr r r If A is an m x n matrix, with columns a1 , a2 ,K , an , an
Columbus State University - MATH - 2115
Section 1.7 Linear IndependenceImportant DefinitionExampleLinear Independence of Matrix ColumnsLinear Independence of Matrix ColumnsSpecial Cases to RememberThus, in this case, we haveGraphicallyLinearly Dependent Sets
Columbus State University - MATH - 2115
Section 1.8 Introduction to Linear TransformationsMatrix TransformationsTerminology:Matrix Transformations A matrix transformation is a transformation T(x)which is computed as a matrix multiplication, that is, a matrix transformation has the
Columbus State University - MATH - 2115
Section 1.9 The Matrix of a Linear TransformationIdentity TransformationMatrix of a Linear TransformationsDefinitionDefinitionExampleTwo More Theorems
Columbus State University - MATH - 2115
Section 2.1 Matrix Operationsj th columni th rowEquality We say that two matrices A and B are equal ifthey have the same size mn and aij=bij for 1 i m and 1 j n.Addition If A and B are 2 mn matrices then A+B is themn matrix with entrie
Columbus State University - MATH - 2115
Section 2.2 The Inverse of a MatrixDefinitionExample1 9 4 -4 A = invertible because there is C = is 2 - 9 2 1 such that AC = CA = I 21 4 9 AC = 2 2 9 - 9 -4 1 CA = 2 - 2 1 -4 0 1 = 1 1 0 4 0 1 = 1 9 0Example
Columbus State University - MATH - 2115
Section 2.3 Characterizations of Invertible MatricesTheorem 8 The Invertible Matrix TheoremInvertible Linear TransformationsDefinitionTheorem 9
Columbus State University - MATH - 2115
Section 2.8 Subspaces ofnDefinition In other words a subspace is closed underaddition and scalar multiplication.Example 1 If v1 and v2 are in Rn andH = Span{v1, v2}, then H is a subspace of Rn. To verify this statement, note that the zer
Columbus State University - MATH - 2115
Section 2.9 Dimension and RankCoordinate Systems The main reason for selecting a basis for asubspace H, instead of merely a spanning set, is that each vector in H can be written in only one way as a linear combination of the basis vectors. To se
Columbus State University - MATH - 2115
Sections 3.1 and 3.2 Introduction to Determinants Properties of DeterminantsNotation Aij is the matrix obtained from matrix A bydeleting the ith row and jth column of A. ExampleNotation Aij is the matrix obtained from matrix A bydeleting the
Columbus State University - MATH - 2115
Sections 5.1 Eigenvectors and EigenvaluesGeometric InterpretationDefinitionGeometric InterpretationDefinition - Eigenspace The eigenspace space of a matrix A correspondingto is the set Eh= {xS Rn : (A- I)x = 0}EigenspaceConclusionCon
Columbus State University - MATH - 2115
Sections 5.2 The Characteristic EquationTheorem The Invertible Matrix Theorem continuedDefinitionDefinition - SimilarityTheorem 4ExampleExample Find p(h) = | A - hI |, the characteristicpolynomial, the eigenvalues, and the eigenvector
Columbus State University - MATH - 2115
Sections 5.3 Diagonalization The goalin this section is to develop a useful factorization A = PDP-1, where A is nn and D is a diagonal matrix (i.e. entries off the main diagonal are all zeros). Then we can use this to compute Ak quickly for larg
Columbus State University - MATH - 2115
Sections 6.1 Inner Product, Length and OrthogonalityNot all linear systems have solutionsGeometric InterpretationInner Product or Dot ProductInner Product or Dot ProductExampleInner Product or Dot ProductLength of a VectorLength of a