Higher Concepts of Mathematics MATRICES AND DETERMINANTSMATRICES AND DETERMINANTSThis chapter will explain the idea of matrices and determinate and the rulesneeded to apply matrices in the solution of simultaneous equations.EO 3.1 DETERMINE the dimensions of a given matrix.EO 3.2 SOLVE a given set of equations using Cramer’s Rule.In the real world, many times the solution to a problem containing a large number of variablesis required. In both physics and electrical circuit theory, many problems will be encounteredwhich contain multiple simultaneous equations with multiple unknowns. These equations can besolved using the standard approach of eliminating the variables or by one of the other methods.This can be difficult and time-consuming. To avoid this problem, and easily solve families ofequations containing multiple unknowns, a type of math was developed called Matrix theory.Once the terminology and basic manipulations of matrices are understood, matrices can be usedto readily solve large complex systems of equations.TheMatrixWe define a matrix as any rectangular array of numbers. Examples of matrices may be formedfrom the coefficients and constants of a system of linear equations: that is,2x - 4y = 73x + y = 16can be written as follows.24 73 1 16The numbers used in the matrix are called elements. In the example given, we have threecolumns and two rows of elements. The number of rows and columns are used to determine thedimensions of the matrix. In our example, the dimensions of the matrix are 2 x 3, having 2 rowsand 3 columns of elements. In general, the dimensions of a matrix which have m rows and ncolumns is called an m x n matrix.Rev. 0 Page 17 MA-05