Matrix Algebra http://elearning.usm.my Md Harashid bin Haron‚ Ph.D. Accounting Section‚ School of Management‚ Universiti Sains Malaysia (USM)‚ 11800 Pulau Pinang‚ Malaysia Email: harashid@usm.my ; mdharashid@gmail.com Matrices? A rectangular array of numbers consisting m horizontal rows and n vertical columns. 5 3 4 2 2 1 6 4 2 A= 5 3 4 2 2 1 6 4 2 A has a size of 3 x 3; 3 x 3 matrix; 3 rows and 3 columns (row is specified
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2. (1.7; 7) Determine if the columns of the matrix form a linear independent set by the definition of linear independence. 1 4 −3 0 −2 −7 5 1 −4 −5 7 5 3. (1.7; 10) Let 1 −2 2 v1 = −5 ‚ v2 = 10 ‚ v3 = −9 −3 6 h (a) For what values of h is v3 in span{v1 ‚ v2}? (b) For what values of h is {v1 ‚ v2‚ v3} a linearly dependent set? 4. (1.8; 24) Suppose vectors v1 ‚ ...‚ vp span Rn‚ and let T : Rn → Rn be a linear transformation. Suppose T (vi ) = 0 for all i = 1‚ ...‚ p. Show
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Chapter 2: Linear Functions Chapter one was a window that gave us a peek into the entire course. Our goal was to understand the basic structure of functions and function notation‚ the toolkit functions‚ domain and range‚ how to recognize and understand composition and transformations of functions and how to understand and utilize inverse functions. With these basic components in hand we will further research the specific details and intricacies of each type of function in our toolkit and use
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a project of your choice‚ either from your own work or as a hypothetical situation. Be sure that you stae your situation first‚ before you develpp the LP model Linear programming is a modeling technique that is used to help managers make logical and informed decisions. All date and input factors are known with certainty. Linear program models are developed in three different steps: Formulation Solution Interpretation The formulation step deals with displaying the problem in a mathematical
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B.Tech. (Computer Science and Engineering) S E M E S T E R C O U R S E FIRST CHM101 PHY101 PHY102 MTH101 HSS-I-1/ ENG112N ESC101 PE101 SECOND TA101 PHY103 MTH102 ESC102 CS100 PE102 THIRD MTH203 CHM201 CS220 ESO-1 ESO211 FOURTH HSS-I-2 TA201 CS201 CS355 OE-1 FIFTH CS330 CS340 ONE OUT OF CS350‚ CS425‚ CS455 SIXTH CS335 CS345 ONE OUT OF CS315‚ CS365‚ CS422 SEVENTH CS498 EIGHTH CS499 In addition to above‚ the student must complete
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Dimensional analysis of models and data sets James F. Pricea) Woods Hole Oceanographic Institution‚ Woods Hole‚ Massachusetts 02543 Received 22 May 2002; accepted 4 November 2002 Dimensional analysis is a widely applicable and sometimes very powerful technique that is demonstrated here in a study of the simple‚ viscous pendulum. The first and crucial step of dimensional analysis is to define a suitably idealized representation of a phenomenon by listing the relevant variables‚ called the physical
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Methods of Mathematical Economics‚ 4rd ed.‚ McGraw-Hill International Edition‚ 2005. COURSE OUTLINE: CHAPTERS 1. Introduction [Note: Read Chaps. 1 & 2 on your own] 1‚ 2 2. Economic Models and Static Analysis 3 3. Elements of Matrix Algebra 4 4. Determinants‚ Singularity‚ Inverse Matrix and Cramer’s Rule 5.1-5.6 5. Input-Output Models 5.7 first exam 6. Comparative Statics and Review of Derivatives 6 7. Rules of Differentiation and the Use in Comparative
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Invertible matrix From Wikipedia‚ the free encyclopedia (Redirected from Nonsingular matrix) Jump to: navigation‚ search In linear algebra an n-by-n (square) matrix A is called invertible (some authors use nonsingular or nondegenerate) if there exists an n-by-n matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case‚ then the matrix B is uniquely determined by A and is called the inverse of A‚
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Directed Line Segment: VECTORS • A line segment with direction is called a directed line segment. • If ‘A’ and ‘B’ are two distinct points in the space‚ then the ordered pair (A‚ B) is called as a directed line segment and is denoted by """""# . ! • In """""# ‚ ‘A’ is called initial point and ‘B’ is called terminal ! point of """""# . ! • The distance from ‘A’ to ‘B’ is called the length or magnitude of """""# . The length or magnitude of """""# ! ! is denoted by ’"""""# ’. Thus
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✎ ✍ 5.2 ✌ Cramer’s Rule Introduction Cramer’s rule is a method for solving linear simultaneous equations. It makes use of determinants and so a knowledge of these is necessary before proceeding. 1. Cramer’s Rule - two equations If we are given a pair of simultaneous equations a1 x + b1 y = d1 a2 x + b2 y = d2 then x‚ and y can be found from d1 b1 d2 b2 a1 b1 a2 b2 a1 d1 a2 d2 a1 b 1 a2 b 2 x= y= Example Solve the equations 3x + 4y = −14 −2x − 3y = 11 Solution Using Cramer’s
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