Matrix Operations SpringSemester 2017

Is a rectangular array of numbers in rows and columns Matrix (matrices) Is a rectangular array of numbers in rows and columns Column 1 Column 2 Column 3 Column 4 Row 1 DEFINITION Row 2 Row 3 Row m

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?

Find the additive inverse: Additive inverse of a matrix. The matrix obtained by changing the sign of every matrix element. The sum of a matrix and its additive inverse is the zero matrix.

ADDITIVE INVERSE OF A MATRIX:

Find the additive identity: The identity property of addition states that when zero is added to any real number, the number does not change.

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

Questions???!!!!

Assignment