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lecture6hout - MATH 006 Calculus and Linear Algebra(Lecture...

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Unformatted text preview: MATH 006 Calculus and Linear Algebra (Lecture 6) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 15 Outline 1 Matrices 2 Linear Systems and Augmented Matrices 3 Row Operations 4 Solving Linear Systems by Row Operations Albert Ku (HKUST) MATH 006 2 / 15 Matrices Matrices Definition A matrix is a rectangular array of numbers written within brackets. Example A = 1- 5 7 0 1 / 2- 1 3 , B =   3 7 6 . 8 2 . 3 1 2 √ 2   . Albert Ku (HKUST) MATH 006 3 / 15 Matrices Some Definitions Definition Each number in a matrix is called an element of the matrix. If a matrix has m rows and n columns, it is called an m × n matrix . A matrix with n rows and n columns is called a square matrix of order n . The position of an element in a matrix is given by the row and the column containing the element. The element on the i th row and j th column is denoted by a ij . The principal diagonal of a matrix A consists of the element a 11 , a 22 , a 33 , . . . . Albert Ku (HKUST) MATH 006 4 / 15 Linear Systems and Augmented Matrices Linear Systems and Augmented Matrices Consider the following linear system:...
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lecture6hout - MATH 006 Calculus and Linear Algebra(Lecture...

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