Learning Objectives<\/p>\n
After reading this chapter, you should be able to<\/p>\n
(1). define what a matrix is.<\/p>\n
(2). identify special types of matrices, and<\/p>\n
(3). identify when two matrices are equal.<\/p>\n
Matrices<\/a> are everywhere. If you have used a spreadsheet such as Excel or written numbers in a table, you have used a matrix. Matrices make presentation of numbers clearer and make calculations easier to program. Look at the matrix below about the sale of tires in a Blowoutr\u2019us store \u2013 given by quarter and make of tires.<\/p>\n Learning Objectives<\/p>\n After reading this chapter, you should be able to:<\/p>\n (1). setup simultaneous linear equations<\/a> in matrix form and vice-versa,<\/p>\n (2). understand the concept of the inverse of a matrix,<\/p>\n (3). know the difference between a consistent and inconsistent system of linear equations, and<\/p>\n 4. learn that a system of linear equations can have a unique solution, no solution or infinite solutions.<\/p>\n Matrix algebra<\/a> is used to solve a system of simultaneous linear equations. In fact, for many mathematical procedures such as the solution to a set of nonlinear equations<\/a>, interpolation, integration, and differential equations, the solutions reduce to a set of simultaneous linear equations. Let us illustrate with an example for interpolation.<\/p>\n Gaussian Elimination Method for Solving Simultaneous Linear Equations<\/p>\n Learning Objectives<\/p>\n After successful completion of this lesson, you should be able to<\/p>\n (1). write the algorithm to solve a set of simultaneous linear equations using Na\u00efve Gauss elimination method<\/p>\n (2). solve a set of simultaneous linear equations using Na\u00efve Gauss elimination.<\/p>\n (3). use the forward elimination steps of Gauss elimination method to find determinant of a square matrix,<\/p>\n (4). enumerate theorems related to determinant of matrices,<\/p>\n (5). relate the zero and non-zero value of the determinant of a square matrix to the existence or non-existence of the matrix inverse.<\/p>\n (6). enumerate the pitfalls of the Na\u00efve Gauss elimination method<\/p>\n (7). show the pitfalls of Na\u00efve Gauss elimination method through examples<\/p>\n (8). write the algorithm to solve a set of simultaneous linear equations using Gaussian elimination<\/a> with Partial Pivoting.<\/p>\n (9). solve a set of simultaneous linear equations using Gauss elimination method with partial pivoting<\/p>\n","protected":false},"excerpt":{"rendered":"System of Equations<\/h3>\n
Matrix algebra is used for solving systems of equations. Can you illustrate this concept?<\/h3>\n