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