1. Chapter 5: Matrices and Determinants Section 5.1: Matrix Addition

2.  Goal: To find the sum and difference of two matrices and the product of a matrix and a scalar

3. Section 5.1: Matrix Addition  Matrix: a rectangular array of numbers written within brackets  Represented by a capital letter  Classified by its dimensions: rows (horizontal) by columns (vertical)  m rows and n columns: m x n “m by n”  A = 2 -1 5 8 0 12

4. Section 5.1: Matrix Addition  Element: each number in a matrix  Each element is identified by its position, given by the row and column number  Square Matrix: a matrix with the same number of rows as columns  Row Matrix: a matrix that has only one row  Column Matrix: a matrix that has only one column

5. Section 5.1: Matrix Addition  Matrix Addition and Subtraction: Can only add/subtract matrices with the same dimensions (if matrices are different sizes their sum or difference is undefined) Ex: A = 2 1 B = 4 6 5 6 0 -7 4 -3 2 -1 Find: A + B and A – B

6. Section 5.1: Matrix Addition  Scalar: any real number when dealing with matrices  Scalar Product: denoted by cA where c is a real number and A is a matrix  EX: Find cA if c = -2 and A = -4 3 2 2 0 -1

7. Section 5.1: Matrix Addition  Example: A = 8 3 and B = -2 0 -4 6 1 5 Find the following: a)-3A b)-3A + 2B c)4B – A

8. Section 5.1: Matrix Addition  Matrix Equation: Use properties of matrix addition and subtraction along with scalar multiplication to solve Ex: If 7[ x y ] = [3x 9] + [12 -2y ]

9. Section 5.1: Matrix Addition  Homework:  Practice Exercises: Pg. 201 #2-26 (even)