41 AN INTRODUCTION TO MATRICES - PowerPoint PPT Presentation

1 / 22
Title:

41 AN INTRODUCTION TO MATRICES

Description:

4-8 BOX-AND-WHISKER PLOTS. Define. Range. Lower quartile. Upper quartile. Interquartile range. Outlier. B. Box-and-whisker plot ... – PowerPoint PPT presentation

Number of Views:2697
Avg rating:3.0/5.0
Slides: 23
Provided by: fcusd8
Category:
Tags:
Transcript and Presenter's Notes

Title: 41 AN INTRODUCTION TO MATRICES

1
4-1 AN INTRODUCTION TO MATRICES
• Define
• Matrix 6. Transformation
• Element 7. Dilation
• Row
• Column
• Matrix Dimensions
• Coordinate Matrix

2
• B. Scalar Multiplication
• C. Solving Matrices

3
• B. Scalar Multiplication
• C. Solving Matrices

4
• B. Scalar Multiplication
• C. Solving Matrices

5
• Steps
• Must have same dimensions
• Add or Subtract the corresponding elements
• Examples

6
(No Transcript)
7
4-3 MULTIPLYIING MATRICES
• Dimension Requirements
• (A m x n )(B n x r) (AB) m x r
• A columns must B rows
• Result an m x r matrix

8
• B. Procedure
• Multiply each element in row 1 of matrix A with
each corresponding element in in column 1 of
matrix B
• Repeat steps 12 for all columns of matrix B.
• Repeat steps 1-3 for all rows of matrix A. these
results are placed in a new row

9
• C. Examples

10
4-4 MATRICES AND DETERMINANTS
• Define
• Third-order Determinant
• B. Expansion by minors
• C. Using Diagonals
• D. Area of a triangle

11
• E. Examples

12
4-5 IDENTITY AND INVERSE MATRICES
• Identity Matrix for Multiplication
• Inverse of a 2x2 Matrix
• Examples
• Find the inverse

13
• C. Examples (cont.)
• Determine if true or false

14
4-6 USING MATRICES TO SOLVE SYSTEMS OF EQUATIONS
• A. Review Solving

15
4-6 USING MATRICES TO SOLVE SYSTEMS OF EQUATIONS
• A. Review Solving

16
4-6 USING MATRICES TO SOLVE SYSTEMS OF EQUATIONS
• A. Review Solving

17
• B. Steps
• Write equations in Standard Form
• Write the system using matrices
• Write using a coefficient matrix and a variable
matrix
• Find the inverse of the coefficient matrix
• Multiply both sides by the inverse
• Check

18
• C. Examples

19
4-7 USING AUGMENTED MATRICES
• Define
• Augmented matrix
• Reducing a matrix
• Row Operations
• Two rows can be interchanged
• A row can be multiplied by a number
• A row can be added to another row

20
• C. Examples
• x 2y z -7
• 2x 2y z 6
• x y 2z -6
• 6r s 9
• 3r -2s

21
4-8 BOX-AND-WHISKER PLOTS
• Define
• Range
• Lower quartile
• Upper quartile
• Interquartile range
• Outlier

22
• B. Box-and-whisker plot