section11 (2) - Linear Equations and Matrices MAT188H1F...

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Unformatted text preview: Linear Equations and Matrices MAT188H1F Lec03 Burbulla Chapter 1 Lecture Notes Fall 2007 Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla Linear Equations and Matrices Linear Equations and Matrices Matrices Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla Linear Equations and Matrices Matrices What is a Matrix? A matrix is a rectangular array of numbers, enclosed in brackets. For example, 3 5 2- 1 6 is a matrix. So is 6 4 2 2 8 2- 4 6 4 The brackets used for a matrix are usually square [ ··· ] as in Nicholson’s book, or round ( ··· ) . But never use straight lines: |···| . In this course, the entries of a matrix will always be real numbers, but they could be complex numbers. Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla Linear Equations and Matrices Matrices Matrix Notation Matrices are usually denoted by capital letters. For instance, we could write A = 3 5 2- 1 6 or B = 6 4 2 2 8 2- 4 6 4 . As we shall see, certain letters are reserved for certain matrices. For instance, O will always denote a zero matrix, and I will always denote an identity matrix. Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla Linear Equations and Matrices Matrices The Size of a Matrix A matrix is said to be m × n if it has m rows, and n columns. For example, A = 3 5 2- 1 6 is a 2 × 3 matrix, and B = 6 4 2 2 8 2- 4 6 4 is a 3 × 3 matrix. The number of entries in an m × n matrix is mn ; so A has 6 entries, and B has 9 entries. Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla Linear Equations and Matrices Matrices Column Matrices and Row Matrices An m × 1 matrix is called a column matrix, or a column vector....
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This note was uploaded on 06/22/2008 for the course ENGINEERIN MAT188 taught by Professor Burbula during the Fall '07 term at University of Toronto- Toronto.

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section11 (2) - Linear Equations and Matrices MAT188H1F...

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