Matrix Operations.

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Presentation transcript:

Matrix Operations

4.1 Questions to answer What is a matrix? How is it read? What is the dimension? What is scalar multiplication? How is it done? What are four properties of matrices?

What is a Matrix? MATRIX: A rectangular arrangement of numbers in rows and columns. The ORDER of a matrix is the number of the rows and columns. The ENTRIES are the numbers in the matrix. This order of this matrix is a 2 x 3. columns rows

Matrix (matrices) DEFINITION Row 1 Row 2 Row 3 Row m Column 1 Column 2

Example: Find the dimensions. A matrix of m rows and n columns is called a matrix with dimensions m x n. Example: Find the dimensions. 2 X 3 3 X 3 2 X 1 1 X 2

PRACTICE: Find the dimensions. 3 X 2 2 X 2 3 X 3 1 X 2 2 X 1 1 X 1

ADDITION and SUBTRACTION of MATRICES

To add matrices, we add the corresponding elements To add matrices, we add the corresponding elements. They must have the same dimensions. A + B

To subtract matrices, we subtract the corresponding elements To subtract matrices, we subtract the corresponding elements. The matrices must have the same dimensions.

PRACTICE PROBLEMS:

Scalar Multiplication: We multiply each # inside our matrix by k.

Examples:

What are your QUESTIONS?

Solving a Matrix Equation Solve for x and y: Solution Step 1: Simplify

Scalar Multiplication:

6x+8=26 6x=18 x=3 10-2y=8 -2y=-2 y=1

Properties of Matrix Operations p. 201 Let A,B, and C be matrices with the same dimension: Associative Property of Addition (A+B)+C = A+(B+C) Commutative Property of Addition A+B = B+A Distributive Property of Addition and Subtraction S(A+B) = SA+SB S(A-B) = SA-SB NOTE: Multiplication is not included!!!

Questions???!!!!

4.1 Questions to answer What is a matrix? How is it read? What is the dimension? A matrix is a rectangular arrangement of numbers in rows and columns. It is read by the rows and columns and the dimension tells the number of rows by columns. What is scalar multiplication? How is it done? Scalar multiplication is the “distributive law” for matrices. What are four properties of matrices? Associative for addition, commutative for addition, distributive for addition, and distributive for subtraction.

Assignment p. 203, 12-36 even, 37-41