Matrices and Matrix Solutions - PowerPoint PPT Presentation

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Matrices and Matrix Solutions

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Matrices and Matrix Solutions Solving Equations With Matrices Fundamental Concepts Types of Matrices Matrix Types, Continued Matrix Types, Continued Matrix Transpose ... – PowerPoint PPT presentation

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Title: Matrices and Matrix Solutions


1
Matrices and Matrix Solutions
2
Solving Equations With Matrices
3
Fundamental Concepts
4
Types of Matrices
5
Matrix Types, Continued
6
Matrix Types, Continued
7
Matrix Transpose
Process of interchanging rows and columns
8
Matrix Equality
9
Matrix Addition
10
Matrix Addition Properties
I. COMMUTATIVE PROPERTY A B B A II.
ASSOCIATIVE PROPERTY A (BC) (A B)
C NOTE Thus order of operation in addition is
not important!
11
Matrix Multiplication
12
Matrix Multiplication Properties
13
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14
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15
Representing Equations Using Matrices
16
Solving Equations By Matrix Inverse
17
Example of Matrix Solution
18
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19
Inverse of a 2x2 Matrix
Note the determinant of A is
Steps 1. Flip the diagonals, 2. Negate the
off-diagonals, and 3. Divide by the
determinant. 4. Matrix is SINGULAR when
determinant 0, and thus has no inverse.
20
Other Methods of Matrix Solution
  • Inverse by elementary row transformations
  • Gaussian elimination
  • Others
  • For large matrices with many zeros, sparse matrix
    methods can be used

21
Spreadsheet Functions
  • TRANSPOSE
  • MMULT
  • MINVERSE
  • The trick in Excel is to press
    ltCtrlgtltShiftgtltEntergt simultaneously
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