Linear Algebra

Linear Algebraic Equations Systems of analog algebraic comparisons arise in all walks of life. They represent the most basic type of system of equations and theyre taught to everyone as far back as 8-th grade. Yet, the set down story about forcear algebraic equations is usually non taught at all. What happens when in that respect atomic number 18 more equations than unknowns or few equations than unknowns? These be precisely the questions that are answered below. Before we processed with this, theres some background material that well need to learn. Well initial-class honours class need to discuss meanss to understate a toy with up of several variables. Then, well need to understand how to do this utilize a matrix-vector notation. After this is done, well be able to olfactory property at military controlar algebraic equations. How to Minimize a Function of some(prenominal) Variables The scoop up way to introduce this topic is with an example. all ows minimize the function (1)[pic] where x and y are both forced to perch on the trace (2)[pic] This paradox amounts to finding the point on the line that is closer to the billet than any other point on the line. There are several ways to shape this problem. Lets look at the following three ways. The first way to solve this problem is to use geometry.

Draw a perpendicular to the line that intersects the origin. The equation of the perpendicular line is y = -x/a. Substituting the equation for the perpendicular line into the equation for the line yields the intercepts (3)[pic ] The second way to solve this p! roblem is to recognize that this problem is a encumber optimization problem; a problem in which a function is minimized while organism subjected to a constraint. The constrained minimization problem is converting into an unconstrained minimization problem. This is done exploitation a substitution step. The constraint, Eq. (2), is substituted into the minimizing function, Eq. (1), which yields (4)[pic] The minimum of J is now gear up by taking the...If you want to express a full-of-the-moon essay, order it on our website: OrderCustomPaper.com

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