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Section 3.1: Matrices Section 3.2: Matrix Multiplication Math 1010 - Chapter 3: Matrices and Matrix Multiplication Sections 3.1, 3.2 Liliana Menjivar Liliana Menjivar Chapter 3: Matrices and Linear Systems of Equations
Section 3.1: Matrices Section 3.2: Matrix Multiplication Table of contents Section 3.1: Matrices Dimension m × n Matrix Special Matrices Multiplying by Scalars Adding and Subtracting Matrices Transpose of a Matrix Section 3.2: Matrix Multiplication Method Properties Powers of a matrix Liliana Menjivar Chapter 3: Matrices and Linear Systems of Equations
Section 3.1: Matrices Section 3.2: Matrix Multiplication A Matrix is a rectangular array of values enclosed in parentheses. Examples: 0 3 1 4 2 5 6 5 , 1 2 3 4 , 1 2 3 4 Notice that each example has a specific number of rows and columns. Liliana Menjivar Chapter 3: Matrices and Linear Systems of Equations
Section 3.1: Matrices Section 3.2: Matrix Multiplication Dimension Columns of a matrix are numbered left to right and rows are numbered top to bottom. The dimensions of a matrix are the numbers m and n that represent the number of rows and columns of a matrix. A matrix is m by n if it has m rows and n columns. Example 1. Give the dimensions of the examples in the previous slide. Liliana Menjivar Chapter 3: Matrices and Linear Systems of Equations
Section 3.1: Matrices Section 3.2: Matrix Multiplication m × n Matrix We denote a general m × n matrix by A m × n A m × n = [ a ij ] m × n = a 11 a 12 · · · a 1 n a 21 a 22 · · · a 2 n . . . . . . . . . a m 1 a m 2 · · · a mn In total there are mn numbers (or entries). We use a ij to denote the value in the i -th row and the j -th column pf A . (eg: a 23 = the value in the 2nd row and the 3rd column) Liliana Menjivar Chapter 3: Matrices and Linear Systems of Equations
Section 3.1: Matrices Section 3.2: Matrix Multiplication Special Matrices A matrix with only one row can be called a row matrix . A matrix with only one column can be called a column matrix . A matrix with the same number of rows and columns ( m = n ) is square . Liliana Menjivar Chapter 3: Matrices and Linear Systems of Equations
Section 3.1: Matrices Section 3.2: Matrix Multiplication Special Matrices 1 2 3 6 1 5 0 - 1 5 2 1 - 1 - 3 5 0 0 - 10 Liliana Menjivar Chapter 3: Matrices and Linear Systems of Equations
Section 3.1: Matrices Section 3.2: Matrix Multiplication Special Matrices