Sec 4.1

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Sec 4.1
Matrices
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Matrix (matrices)
A rectangular array of numbers
Column 4
Column 1
Column 2
Column 3
Row 1
DEFINITION
Row 2
Row 3
Row m
Dimensions Rows x Columns
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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
1 x 2
2 x 1
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Equal Matrices

• Two matrices are equal if they have the same
  dimensions the corresponding entries are
  equivalent
• Algebraically

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ADDITION 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.
They must have the same dimensions
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ADDITIVE INVERSE OF A MATRIX
A matrix with the same dimensions, but the
entries are the exact opposite
Whats the additive inverse of A ?
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Scalar Multiplication
Multiply each inside the matrix by a real , k,
outside the matrix
Think of the distributive property!
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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
Write equations solve
6x 8 26 6x 18 x 3
10 2y 8 -2y -2 y 1
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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!!!

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Questions???!!!!