Matrices and Matrix Solutions

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Matrices and Matrix Solutions
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Solving Equations With Matrices
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Fundamental Concepts
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Types of Matrices
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Matrix Types, Continued
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Matrix Types, Continued
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Matrix Transpose
Process of interchanging rows and columns
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Matrix Equality
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Matrix Addition
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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!
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Matrix Multiplication
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Matrix Multiplication Properties
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Representing Equations Using Matrices
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Solving Equations By Matrix Inverse
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Example of Matrix Solution
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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.
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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

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Spreadsheet Functions

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