tailieunhanh - Ebook MATLAB for engineers (3/E): Part 2

Part 2 book “MATLAB for engineers” has contents: Matrix algebra, other kinds of arrays, symbolic mathematics, numerical techniques, advanced graphics creating graphical user interfaces, simulink a brief introduction. | CHAPTER 10 Matrix Algebra Objectives After reading this chapter, you should be able to: • Perform the basic operations of matrix algebra • Solve simultaneous equations by using MATLAB® matrix operations • Use some of MATLAB®’s special matrices INTRODUCTION The terms array and matrix are often used interchangeably in engineering. However, technically, an array is an orderly grouping of information, whereas a matrix is a twodimensional numeric array used in linear algebra. Arrays can contain numeric information, but they can also contain character data, symbolic data, and so on. Thus, not all arrays are matrices. Only those upon which you intend to perform linear transformations meet the strict definition of a matrix. Matrix algebra is used extensively in engineering applications. The mathematics of matrix algebra is first introduced in college algebra courses and is extended in linear algebra courses and courses in differential equations. Students start using matrix algebra regularly in statics and dynamics classes. MATRIX OPERATIONS AND FUNCTIONS In this chapter, we introduce MATLAB® functions and operators that are intended specifically for use in matrix algebra. These functions and operators are contrasted with MATLAB®’s array functions and operators, from which they differ significantly. Much of this material may be a review, but is included for completeness. 344 Chapter 10 Matrix Algebra Transpose ARRAY An orderly grouping of information The transpose operator changes the rows of a matrix into columns and the columns into rows. In mathematics texts, you will often see the transpose indicated with superscript T (as in AT ). Don’t confuse this notation with MATLAB® syntax, however: In MATLAB®, the transpose operator is a single quote ('), so that the transpose of matrix A is A'. Consider the following matrix and its transpose: 1 4 A ≥ 7 10 2 5 8 11 3 1 6 T ¥ A ≥2 9 3 12 4 3 6 7 8 9 10 11 ¥ 12 The rows and columns have been .