Chapter 4 - Matrices

Abstract

This chapter deals with matrices, which is an ordered set of values. The row is one of the horizontal lines of numbers and the column is the vertical lines. If the matrix has “m” rows and “n” columns, then the matrix is an “m X n” matrix. If m=n, it is a square matrix. Determinants can come only from square matrices. The quantities within the matrix are called the elements of the matrix. Two matrices are identical if each of the elements is identical. Unequal matrices may have the same determinant, and equal matrices have the same determinant. The value of the determinant is calculated by combining the products of the terms in the diagonals. Matrices can be added or subtracted but, must be of the same size. To add “A” and “'B matrices,” a new matrix “C” is made, where each element of “C” is the sum of the same elements in “A” and “B.” A diagonal matrix is one where all elements are zero except on the main diagonal. Multiplying a scalar matrix times another matrix of proper size increases the value of each element of that matrix by the value of the element of the scalar matrix. If the elements in a diagonal matrix equals to one, then it is an identity matrix. Multiplying a matrix by an identity matrix does not change its value. If rows and columns in a matrix are interchanged, then it is a transpose of that matrix.