lect136_4_w09 - Monday January 12 - Lecture 4 : Matrices...

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Monday January 12 Lecture 4 : Matrices (Refers to section 3.1) Expectations: 1. Define the operation of addition, multiplication, scalar multiplication and transposition on matrices. 2. Use the rules of matrix algebra. (Hand-out) 3. Define identity matrix, zero matrix 4. Express the dot-product of two vectors as a product of two matrices. We have previously spoken of "matrix" but only as related to a system of linear equations (coefficient matrix of a system and augmented coefficient matrix of a system) . In this lecture we define the notion of a matrix (simply a rectangular array of numbers) independently of a system of linear equations. We define operations on matrices and then, once again, find a new way of representing a system of linear equations, namely a matrix equation . 4.1 Definition Matrices . If m and n are positive integers, a matrix of size m × n (or of dimension m × n ), is a rectangular array of real numbers, arranged in m rows and n columns and is represented as A = [ a ij ] m × n The symbol i is called the row index and j is called the column index . The a ij 's are called the entries or components of the matrix. Example : This is a 3 by 3 matrix A : a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 4.1.1 Two matrices are said to be equal matrices if their corresponding entries are equal. Clearly matrices of different dimensions cannot be equal. 4.1.2 Remark Distinction between vectors and matrices :
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o When we think in terms of " vectors " then (2, 1, 7) and the numbers 2, 1, 7 written in a column are viewed as being equal in R 3 . o
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lect136_4_w09 - Monday January 12 - Lecture 4 : Matrices...

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