Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Lesson 12.1 – Adding and Subtracting Matrices CHAPTER 12 - MATRICES Take notes in your notebook. Work the problems in your notebook BEFORE advancing to the solutions. A MATRIX A matrix is a rectangular arrangement of numbers into rows and columns. 4 -2 9 0 3 -5 This is a 2 by 3 Matrix. A MATRIX 2 Rows and 3 Columns 4 0 -2 3 9 -5 VOCABULARY Matrix - a rectangular array of variables or numbers in horizontal rows and vertical columns enclosed in brackets. Element - each value in a matrix; either a number or a constant. Dimension - number of rows by number of columns of a matrix. **A matrix is named by its dimensions. FIND THE DIMENSIONS OF EACH MATRIX. 2 1. A = 0 4 1 5 8 Dimensions: 3x2 1 2 2. B = 3 4 Dimensions: 4x1 0 5 3 1 3. C = 2 0 9 6 Dimensions: 2x4 FIND THE DIMENSIONS OF EACH MATRIX. 8 0 10 1 3 0 2 4 3 2 1 7 0 1 3 1 0 4 6 5 9 2 7 3 x 3 (or square matrix) 3 8 6 3x5 1 2x2 2 (aka: square matrix) 9 5 7 0 1x4 (aka: row matrix) 9 7 0 6 4x1 (aka: column matrix) DIFFERENT TYPES OF MATRICES Column Matrix – 9 7 a matrix with only one column. 0 Row Matrix – 6 9 5 7 0 a matrix with only one row. Square Matrix – a matrix that has the same number of rows and columns. 1 1 0 2 ADDING MATRICES 1.) -3 -2 5 -7 6 -8 -9 6 Add the corresponding elements of each matrix. ADDING MATRICES To add two matrices, they must have the same dimensions. To add, you simply add corresponding elements. 5 3 0 3 2 4 3 7 4 1 0 3 Working matrix 5 (2) 3 1 3 3 4 0 0 4 7 (3) Answer Matrix 3 0 4 2 4 4 ADDING MATRICES 4 0 -2 3 2x3 9 -5 -1 0 3 7 2x2 Matrices can only be added if they have the same # of rows & columns ADDING MATRICES 8 0 1 3 1 7 5 4 2 9 5 3 = 5 2 3 2 8 (1) 07 1 5 3 2 5 5 43 23 9 ( 2) = 7 0 7 7 4 5 5 7 Solution matrix Working matrix SUBTRACTING MATRICES 1.) -3 -2 5 -7 6 -8 -9 6 Subtract the corresponding elements of each matrix. SUBTRACTING MATRICES To subtract two matrices, they must have the same dimensions. You simply subtract corresponding elements. Working matrix 9 2 4 4 0 7 9 4 5 0 6 1 5 4 5 1 1 3 8 2 3 2 1 (2) 5 4 3 20 47 0 5 6 (4) 33 8 2 Solution matrix 2 5 0 3 10 6 SUBTRACTING MATRICES = 2 8 1 4 3 0 1 0 7 3 1 5 0 4 2 Working matrix 2-0 -4-1 8-3 3-8 0-(-1) -7-1 1-(-4) 5-2 0-7 = 8 1 7 Solution matrix 2 -5 -5 5 1 -8 5 3 -7 YOU TRY THESE 1.) -3 -2 5 -7 2.) 3 -7 7 -1 3.) -5 7 -3 -9 6 -8 -9 6 4 -3 7 8 -6 5 -1 7 YOU TRY THESE (SOLUTIONS) 1.) -3 -2 5 -7 2.) 3 -7 7 -1 3.) -5 7 -3 -9 6 -8 -9 6 4 -3 7 8 -6 5 -1 7 3 -10 -4 -1 7 -10 14 1 7 2 -2 -16 YOU TRY THESE 4.) 0 -3 -1 4 5.) 1 1 1 1 6.) -5 7 -3 -9 -6 0 3 1 4 -3 7 0 5 -7 3 9 YOU TRY THESE (SOLUTIONS) 4.) 0 -3 -1 4 5.) 1 1 1 1 6.) -5 7 -3 -9 -6 3 4 7 5 3 0 1 -3 0 -7 9 6 -3 -4 -2 -3 4 -6 1 0 0 0 0 CLASS WORK Read Lesson 12.1 “Adding and Subtracting Matrices” in your textbook and review the Power Point lesson again. Complete the 12.1 Vocabulary Worksheet Review and complete the 12.1 Reteaching Worksheet HOMEWORK In your textbook: Lesson 12.1/ 7- 17odd, 19-29 MATRIX LOGIC Jim, Mario and Mike are married to Shana, Kelly and Lisa. Mario is Kelly’s brother and lives in Florida with his wife. Mike is shorter than Lisa’s husband. Mike works at a bank. Shana and her husband live in Kentucky. Kelly and her husband work in a candy store. Who is married to whom? Jim Shana Kelly Lisa Mario Mike X X O O X X O X X