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chapter3.page01 - A to denote a matrix and lower case...

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CHAPTER 1 Brief Introduction to Vectors and Matrices In this chapter, we will discuss some needed concepts found in in- troductory course in linear algebra. We will introduce matrix, vector, vector-valued function, and linear independency of a group of vectors and vector-valued functions. 1. Vectors and Matrices A matrix is a group of numbers(elements) that are arranged in rows and columns. In general, an m × n matrix is a rectangular array of mn numbers (or elements) arranged in m rows and n columns. If m = n the matrix is called a square matrix. For example a 2 × 2 matrix is a 11 a 12 a 21 a 22 and an 3 × 3 matrix is a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 Generally, we use bold phase letter, like
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Unformatted text preview: A , to denote a matrix, and lower case letters with subscripts, like a ij , to denote element of a matrix. Here a ij would be the element at i th row and j th column. So a 11 is an element at 1 st row and column. Sometime we use the abbreviation A = ( a ij ) for a matrix with elements a ij . 1.1. Special matrices. 0 denotes the zero matrix whose elements are all zeroes. So 2 × 2 and 3 × 3 zero matrices are • 0 0 0 0 ‚ and 0 0 0 0 0 0 0 0 0 Another special matrix is the identity matrix, denoted by I , a iden-tity matrix is an matrix whose main diagonal elements are 1, and all 1...
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