Matrix Operations

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Matrix Operations
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4.1 Questions to answer

• What is a matrix? How is it read? What is the
  dimension?
• What is scalar multiplication? How is it done?
• What are four properties of matrices?

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What is a Matrix?

• MATRIX A rectangular arrangement of numbers in
  rows and columns.
• The ORDER of a matrix is the number of the rows
  and columns.
• The ENTRIES are the numbers in the matrix.

• This order of this matrix is a 2 x 3.

columns
rows
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Matrix (matrices)
Column 4
Column 1
Column 2
Column 3
Row 1
DEFINITION
Row 2
Row 3
Row m
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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. They must have the same dimensions.
A B
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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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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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6x826 6x18 x3
10-2y8 -2y-2 y1
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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 (AB)C
  A(BC)
• Commutative Property of Addition AB BA
• Distributive Property of Addition and
  Subtraction S(AB) SASB S(A-B) SA-SB
• NOTE Multiplication is not included!!!

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Questions???!!!!
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4.1 Questions to answer

• What is a matrix? How is it read? What is the
  dimension?
• A matrix is a rectangular arrangement of numbers
  in rows and columns. It is read by the rows and
  columns and the dimension tells the number of
  rows by columns.
• What is scalar multiplication? How is it done?
• Scalar multiplication is the distributive law
  for matrices.
• What are four properties of matrices?
• Associative for addition, commutative for
  addition, distributive for addition, and
  distributive for subtraction.

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Assignment
p. 203, 12-36 even, 37-41