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Matrices and Determinants

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Elementary Linear Algebra Anton & Rorres, 9th Edition

Matrices A matrix is a rectangular array of quantities (numbers, expressions or function), arranged in m rows and n columns x 3y.

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Chapter 12 - Matrices

Sep 12, 2014

10.19k likes | 23.71k Views

Lesson 12.1 – Adding and Subtracting Matrices. Take notes in your notebook. Work the problems in your notebook BEFORE advancing to the solutions. Chapter 12 - Matrices. A matrix is a rectangular arrangement of numbers into rows and columns . 4 -2 9 0 3 -5. A Matrix.

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• column matrix
• square matrix
• aka column matrix
• aka row matrix

Presentation Transcript

Lesson 12.1 – Adding and Subtracting Matrices Take notes in your notebook. Work the problems in your notebook BEFORE advancing to the solutions. Chapter 12 - Matrices

A matrix is a rectangular arrangement of numbers into rows and columns. 4 -2 9 0 3 -5 A Matrix This is a 2 by 3 Matrix.

2 Rows and 3 Columns 4 -2 9 0 3 -5 A Matrix

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. Vocabulary

Find the dimensions of each matrix. Dimensions: 3x2 Dimensions: 4x1 Dimensions: 2x4

Find the dimensions of each matrix. (or square matrix) 3 x 3 1 x 4 (aka: row matrix) 3 x 5 4 x 1 2 x 2 (aka: column matrix) (aka: square matrix)

Column Matrix – a matrix with only one column. Row Matrix – a matrix with only one row. Square Matrix – a matrix that has the same number of rows and columns. Different types of Matrices

1.) -3 -2 6 -8 5 -7 -9 6 Adding Matrices + = 3 -10 -4 -1 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. Working matrix Answer Matrix

4 -2 9 -1 0 0 3 -5 3 7 Matrices can only be added if they have the same # of rows & columns Adding Matrices + 2 x 3 2 x 2

Adding Matrices Working matrix = 7 7 4 5 Solution matrix = 0 7 5 7

1.) -3 -2 6 -8 5 -7 -9 6 Subtracting Matrices - = -9 6 14 -13 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 Solution matrix

Subtracting Matrices Working matrix Solution matrix 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

1.) -3 -2 6 -8 5 -7 -9 6 2.) 3 -7 4 -3 7 -1 7 8 3.) -5 7 -6 5 -3 -9 -1 7 You try these + = = + = -

1.) -3 -2 6 -8 5 -7 -9 6 2.) 3 -7 4 -3 7 -1 7 8 3.) -5 7 -6 5 -3 -9 -1 7 You try these (Solutions) 3 -10 -4 -1 = + 7 -10 14 7 = + 1 2 -2 -16 = -

4.) 0 -3 -6 0 -1 4 3 1 5.) 1 1 4 -3 1 1 7 0 6.) -5 7 5 -7 -3 -9 3 9 You try these = - = - = +

4.) 0 -3 -6 0 6 -3 -1 4 3 1 -4 -2 5.) 1 1 4 -3 -3 4 1 1 7 0 -6 1 6.) -5 7 5 -7 0 0 -3 -9 3 9 0 0 You try these (Solutions) = - = - = +

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 Class work

In your textbook: Lesson 12.1/ 7- 17odd, 19-29 Homework

Matrix Logic Jim Mario Mike Shana Kelly Lisa 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? X X O O X X X O X

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