PPT-MATH 374 Lecture 21 Chapter 8: Linear Systems of Equations

2 81 First Order Systems We now look at systems of linear differential equations One of the main reasons is that any nth order differential equation with n gt 1 can be written as a first order system of n equations in n unknown functions. They are also referred to as Linear TimeInvariant systems in case the independent variable for the input and output signals is time Remember that linearity means that is t and t are responses of the system to signals t and t respectively then the re e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations . L. 1. , . L. ∞. . Norm Problems. and. Linear Programming. Syllabus. Lecture 01 Describing Inverse Problems. Lecture 02 Probability and Measurement Error, Part 1. Lecture 03 Probability and Measurement Error, Part 2 . 3.1 – . Systems of Linear Equations in Two Variables. 1. Suppose we have two linear equations. :. . . Together, they make a ________________________________ (also called a . ___________________).. By graphing. Definition. A system of linear equations, aka linear system, consists of two or more linear equations with the same variables.. x + 2y = 7. 3x – 2y = 5. The solution. The solution of a system of linear equations is the ordered pair that satisfies each equation in the system. . Algebra 2. Chapter 3. This Slideshow was developed to accompany the textbook. Larson Algebra 2. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. 1. 2. Elementary Row Operations. There are three kinds of Elementary Row Operations.. 1) Interchanging two rows.. Multiplying a row by a non-zero constant.. Adding a multiple of one row to another row.. MAT 275. Ordinary vs. Partial. If the differential equation consists of a function of the form . y. = . f . (. x. ) and some combination of its derivatives, then the differential equation is . ordinary. Algebra 1: Unit 7. Graphing linear equations. Graphing Linear Equations. The steps to graphing a linear equation:. Step . 1: Create an x/y chart. Step 2: Pick two points for x. Step 3: Determine the value of y given x. Unit 4. Review:. Slope and Slope-Intercept. Slope and Slope-Intercept Form. Slope-Intercept Form. :. . . is . ______ . and . is the . __________ . of the line.. Graph is a . straight non-vertical line. Objectives:. To solve a system of linear equations by graphing. To classify a system of linear equations as consistent (independent and dependent) or inconsistent. To graph a system of linear inequalities.  .  . Solutions are found at the intersection of the equations in the system.. Types of Solutions. Section 8.1 – Systems of Linear Equations. Consistent System. One solution. Consistent System. Infinite solutions. Mike . Barile. . Professors . Hari. . Koirala. & . Jeanelle. Day. Eastern Connecticut State University . EDU 560. Unit Topic. Solving One Variable Equations. Focus. Evaluating Expressions, Solving and Generating Word Problems . . Norm Problems. and. Linear Programming. Syllabus. Lecture 01 Describing Inverse Problems. Lecture 02 Probability and Measurement Error, Part 1. Lecture 03 Probability and Measurement Error, Part 2 .