41 AN INTRODUCTION TO MATRICES

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4-1 AN INTRODUCTION TO MATRICES

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

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• B. Scalar Multiplication
• C. Solving Matrices

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• B. Scalar Multiplication
• C. Solving Matrices

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• B. Scalar Multiplication
• C. Solving Matrices

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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

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• 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

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• C. Examples

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4-4 MATRICES AND DETERMINANTS

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

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• E. Examples

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4-5 IDENTITY AND INVERSE MATRICES

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

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

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4-6 USING MATRICES TO SOLVE SYSTEMS OF EQUATIONS

• A. Review Solving

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4-6 USING MATRICES TO SOLVE SYSTEMS OF EQUATIONS

• A. Review Solving

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4-6 USING MATRICES TO SOLVE SYSTEMS OF EQUATIONS

• A. Review Solving

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• 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

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• C. Examples

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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

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

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4-8 BOX-AND-WHISKER PLOTS

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

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• B. Box-and-whisker plot