Lect3b - Chapter 1. Matrices and Systems of Equations...

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Unformatted text preview: Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Goal Augmented matrices leads to consider rectangular arrays of numbers - matrices. A = a 1 1 a 1 2 ··· a 1 n a 2 1 a 2 2 ··· a 2 n . . . . . . . . . . . . a m 1 a m 2 ··· a m n Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Goal Augmented matrices leads to consider rectangular arrays of numbers - matrices. A = a 1 1 a 1 2 ··· a 1 n a 2 1 a 2 2 ··· a 2 n . . . . . . . . . . . . a m 1 a m 2 ··· a m n Goal Introduce arithmetic operations on matrices Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Matrices Definition A matrix is a rectangular array of numbers. A = a 1 1 a 1 2 ··· a 1 n a 2 1 a 2 2 ··· a 2 n . . . . . . . . . . . . a m 1 a m 2 ··· a m n Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Matrices Definition A matrix is a rectangular array of numbers. A = a 1 1 a 1 2 ··· a 1 n a 2 1 a 2 2 ··· a 2 n . . . . . . . . . . . . a m 1 a m 2 ··· a m n We say A has m rows , n columns . The dimension (or size ) of A is m × n ( m-by- n ). The element a i j is called the ( i , j ) th entry . Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Vectors A is called a square matrix of order n if m = n . An 1 × n matrix is called a row vector . An m × 1 matrix is called a column vector . Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Vectors A is called a square matrix of order n if m = n . An 1 × n matrix is called a row vector . An m × 1 matrix is called a column vector . Question Why call it a vector? Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Vectors A is called a square matrix of order n if m = n . An 1 × n matrix is called a row vector . An m × 1 matrix is called a column vector . Question Why call it a vector? Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Vectors A is called a square matrix of order n if m = n . An 1 × n matrix is called a row vector . An m × 1 matrix is called a column vector . Question Why call it a vector? We may represent it as ( 2 1 ) or 2 1 . Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Vectors A is called a square matrix of order n if m = n . An 1 × n matrix is called a row vector . An m × 1 matrix is called a column vector . Question Why call it a vector?...
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This note was uploaded on 09/06/2010 for the course MATH MATH1111 taught by Professor Forgot during the Fall '08 term at HKU.

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Lect3b - Chapter 1. Matrices and Systems of Equations...

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