Sec 4.1 Matrices.

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Presentation transcript:

Sec 4.1 Matrices

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

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

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

ADDITION & SUBTRACTION of MATRICES

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

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

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 ?

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

Examples:

What are your QUESTIONS?

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

Scalar Multiplication: Write equations & solve: 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 k(A + B) = kA + kB k(A – B) = kA – kB NOTE: Multiplication is not included!!!

Questions???!!!!