3.5 Perform Basic Matrix Operations Algebra II

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

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 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!!!

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