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4-1 AN INTRODUCTION TO MATRICES

- Define
- Matrix 6. Transformation
- Element 7. Dilation
- Row
- Column
- Matrix Dimensions
- Coordinate Matrix

- B. Scalar Multiplication
- C. Solving Matrices

- B. Scalar Multiplication
- C. Solving Matrices

- B. Scalar Multiplication
- C. Solving Matrices

4-2 ADDING AND SUBTRACTING MATRICES

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

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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

- B. Procedure
- Multiply each element in row 1 of matrix A with

each corresponding element in in column 1 of

matrix B - Add the values answer element
- Repeat steps 12 for all columns of matrix B.

Answers in same row. - Repeat steps 1-3 for all rows of matrix A. these

results are placed in a new row

- C. Examples

4-4 MATRICES AND DETERMINANTS

- Define
- Third-order Determinant
- B. Expansion by minors
- C. Using Diagonals
- D. Area of a triangle

- E. Examples

4-5 IDENTITY AND INVERSE MATRICES

- Identity Matrix for Multiplication
- Inverse of a 2x2 Matrix
- Examples
- Find the inverse

- C. Examples (cont.)
- Determine if true or false

4-6 USING MATRICES TO SOLVE SYSTEMS OF EQUATIONS

- A. Review Solving

4-6 USING MATRICES TO SOLVE SYSTEMS OF EQUATIONS

- A. Review Solving

4-6 USING MATRICES TO SOLVE SYSTEMS OF EQUATIONS

- A. Review Solving

- 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

- C. Examples

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

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

4-8 BOX-AND-WHISKER PLOTS

- Define
- Range
- Lower quartile
- Upper quartile
- Interquartile range
- Outlier

- B. Box-and-whisker plot