Matrix Operations Ms. Olifer.

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Presentation transcript:

Matrix Operations Ms. Olifer

OBJECTIVES SWBAT: Identify the dimensions of matrices Add and subtract matrices

Matrix - a rectangular array of variables or constants 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.

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. Matrices ROCK!!! Example: Find the dimensions. 2 X 3 3 X 3 2 X 1 1 X 2

MATRICES ROCK!!!

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

Different types of Matrices 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.

Equal Matrices - two matrices that have the same dimensions and each element of one matrix is equal to the corresponding element of the other matrix. *The definition of equal matrices can be used to find values when elements of the matrices are algebraic expressions.

Set each element equal and solve! Ex. Set each element equal and solve!

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

When a zero matrix is added to another matrix of the same dimension, that same matrix is obtained.

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:

ADDITIVE INVERSE OF A MATRIX:

Find the additive inverse:

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 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???!!!!

Assignment