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3.5 Perform Basic Matrix Operations Algebra II
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Matrix (matrices) DEFINITION Row 1 Row 2 Row 3 Row m Column 1 Column 2
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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
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PRACTICE: Find the dimensions.
3 X 2 2 X 2 3 X 3 1 X 2 2 X 1 1 X 1
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ADDITION and SUBTRACTION of
MATRICES
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To add matrices, we add the corresponding elements
To add matrices, we add the corresponding elements. They must have the same dimensions. A + B
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When a zero matrix is added to another matrix of the same dimension, that same matrix is obtained.
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To subtract matrices, we subtract the corresponding elements
To subtract matrices, we subtract the corresponding elements. The matrices must have the same dimensions.
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PRACTICE PROBLEMS:
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ADDITIVE INVERSE OF A MATRIX:
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Find the additive inverse:
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Scalar Multiplication:
We multiply each # inside our matrix by k.
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Examples:
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What are your QUESTIONS?
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Solving a Matrix Equation
Solve for x and y: Solution Step 1: Simplify
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Scalar Multiplication:
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6x+8=26 6x=18 x=3 10-2y=8 -2y=-2 y=1
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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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Questions???!!!!
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Assignment
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