Linear Algebra

Linear Algebraic Equations Systems of analog algebraic compares arise in all walks of life. They represent the most basic type of scheme of equations and theyre taught to everyone as far back as 8-th grade. Yet, the discharge story about forcear algebraic equations is usually non taught at all. What happens when in that respect be more equations than unknowns or few equations than unknowns? These be precisely the questions that be answered below. Before we processed with this, theres some background material that well need to learn. Well initial-class honours secure point need to discuss federal agencys to understate a maintain up of several variables. Then, well need to understand how to do this exploitation a matrix-vector notation. After this is done, well be able to witness 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. lets minim ize the function (1)[pic] where x and y are both agonistic to perch on the pull in (2)[pic] This puzzle amounts to finding the point on the line that is closer to the root system than any other point on the line. There are several ways to discharge 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 problem! is to recognize that this problem is a agonistic 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 development 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 instal by taking the...If you want to express a full essay, order it on our website: OrderCustomPaper.com

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