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## Lesson 7 Matrices

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**Lesson 7 Matrices**NCSCOS Obj.: 1.02; 3.01; 3.02 Objectives: TLW add and subtract Matrices TLW Multiply a Matrix by a Scalar TLW identify and analyze data in a matrix**MATRIX: A rectangular arrangement of numbers in rows and**columns. The DIMENSION of a matrix is the number of the rows and columns. The ENTRIES are the numbers in the matrix. What is a Matrix? • The dimension of this matrix is a 2 x 3. columns rows**What is the Dimension?**(or square matrix) 3 x 3 (Also called a column matrix) 1 x 4 3 x 5 (or square matrix) 2 x 2 4 x 1 (Also called a row matrix)**Adding Two Matrices**• To add two matrices, they must have the same order. To add, you simply add corresponding entries.**=**7 7 4 5 = 0 7 5 7**Subtracting Two Matrices**• To subtract two matrices, they must have the same order. You simply subtract corresponding entries.**2-0**-4-1 3-8 -5 2 -5 8-3 0-(-1) -7-1 5 -8 1 = = 1-(-4) 5-2 0-7 5 3 -7**Multiplying a Matrix by a Scalar**• In matrix algebra, a real number is often called a SCALAR. To multiply a matrix by a scalar, you multiply each entry in the matrix by that scalar.**-3**3 -2 6 -5 -2(-3) -2(3) 6 -6 -12 -2(6) -2(-5) 10**Example 2-1a**State the dimensions of the matrix. Then identify the position of the circled element in the matrix. This matrix has 3 rows and 1 column. Answer: It is a 3-by-1 matrix. The circled element is the second row and the first column.**Example 2-1b**State the dimensions of the matrix. Then identify the position of the circled element in the matrix. This matrix has 3 rows and 4 columns. Answer: It is a 3-by-4 matrix. The circled element is the first row and the fourth column.**State the dimensions of each matrix. Then identify the**position of the circled element in the matrix. a. b. Example 2-1c Answer: 1 by 2; first row, first column Answer: 2 by 4; second row, third column**=**Definition of matrix addition Example 2-2a Find the sum. If the sum does not exist, write impossible.**Answer: = Simplify.**Example 2-2a**Example 2-2b**Find the sum. If the sum does not exist, write impossible. Since the first matrix is a 2 by 2 matrix and the second matrix is a 3 by 3 matrix, the matrices do not have the same dimensions. Answer: It is impossible to add these matrices.**Find the sum. If the sum does not exist, write impossible.**a. b. Answer: Example 2-2c Answer: impossible**Example 2-3a**College Football The Division 1-A current football coaches with the five best overall records as of 2000 are listed below.**Example 2-3a**Use subtraction of matrices to determine the regular season records of these coaches.**Example 2-3a**Answer:**Example 2-3b**Four performing theaters have seating capacities listed below.**Example 2-3b**Use subtraction of matrices to find the seating capacities on the main floors of the theaters. Answer:**Substitution**Definition of scalar multiplication Simplify. Answer: Example 2-4a**Answer:**Example 2-4b