Presentation is loading. Please wait.

Presentation is loading. Please wait.

Sec 4.1 Matrices.

Similar presentations


Presentation on theme: "Sec 4.1 Matrices."— Presentation transcript:

1 Sec 4.1 Matrices

2 Matrix (matrices) DEFINITION Entry or Element
A rectangular array of numbers Column 1 Column 2 Column 3 Column 4 Row 1 Entry or Element DEFINITION Row 2 Row 3 Row m Dimensions: # Rows x # Columns

3 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 1 x 2 2 x 1

4 Equal Matrices Two matrices are equal if they have the same dimensions & the corresponding entries are equivalent Algebraically…

5 ADDITION & SUBTRACTION of
MATRICES

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

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

8 ADDITIVE INVERSE OF A MATRIX:
A matrix with the same dimensions, but the entries are the exact opposite What’s the additive inverse of A ?

9 Scalar Multiplication:
Multiply each # inside the matrix by a real #, k, outside the matrix Think of the distributive property!

10 Examples:

11 What are your QUESTIONS?

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

13 Scalar Multiplication:
Write equations & solve: 6x + 8 = 26 6x = 18 x = 3 10 – 2y = 8 -2y = -2 y = 1

14 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 k(A + B) = kA + kB k(A – B) = kA – kB NOTE: Multiplication is not included!!!

15 Questions???!!!!


Download ppt "Sec 4.1 Matrices."

Similar presentations


Ads by Google