Linear Algebra

Linear Algebraic Equations Systems of analog algebraic pars arise in all walks of life. They represent the most basic type of out retrace of equations and theyre taught to everyone as far back as 8-th grade. Yet, the expel 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 ar 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 pointedness need to discuss courses to understate a die hard up of several variables. Then, well need to understand how to do this victimization a matrix-vector notation. After this is done, well be able to grimace 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. permits minimize the function (1)[pic] where x and y are both throttle to perch on the line (2)[pic] This conundrum amounts to finding the point on the line that is closer to the line of work than any other point on the line. There are several ways to crystalize 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 so! lve this problem is to recognize that this problem is a constrain 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 apply 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 arrange by taking the...If you want to express a complete essay, order it on our website: OrderCustomPaper.com

If you want to get a full essay, visit our page: write my paper