Part 2 book “Mathematics for engineers” has contents: matrices and determinants, using matrices and determinants to solve equations, vectors, differentiation, techniques and applications of differentiation, integration, applications of integration, differential equations, the laplace transform, statistics and probability, and other contents. | Matrices and determinants Chapter 12 A matrix is a rectangular array of numbers or expressions. The plural of matrix is matrices. This chapter deals with the addition, subtraction and multiplication of matrices. Unlike numbers, the processes of addition, subtraction and multiplication can be applied to matrices only under specific conditions. Division of matrices is not defined. However, the inverse of a matrix may be found under certain conditions. The inverse matrix and its calculation are explained in Block 4. Determinants are introduced in Block 3. A determinant is a number that is calculated from the elements of a matrix and is used in finding the inverse matrix. The chapter closes with the application of matrices to computer graphics. Multiplication by a matrix can be interpreted as a transformation of a figure. Chapter 12 contents Block 1 Introduction to matrices Block 2 Multiplication of matrices Block 3 Determinants Block 4 The inverse of a matrix Block 5 Computer graphics End of chapter exercises BLOCK 1 Introduction to matrices Introduction A matrix is a rectangular array of numbers or expressions usually enclosed in brackets. For example, a 3 0 1 -6 9 b, 2 a a g b b, d a 3 - l 7 4 b 6 - l are all matrices. Note that the plural of matrix is matrices. We often denote a matrix by a capital letter, for example 4 A = £ 3 -1 1 1 6 ≥, B = a 6 0 0 1 -1 4 3 b 2 The size of a matrix is given by the number of rows and the number of columns. The matrix A has three rows and two columns and so is described as a 3 * 2 matrix. We say that A is a ‘three by two matrix’. Matrix B has two rows and four columns and so is a 2 * 4 matrix. Notice that the number of rows is always stated first. An n * m matrix has n rows and m columns. The individual numbers or expressions in a matrix are called the elements and are usually denoted by a small letter. For example, for A,
