Matrix Algebra Determinants

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Matrix AlgebraDeterminants

• Math Review

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Matrix Algebra

• Determinant - The Result
• Order - Size
• Second Order is 2 X 2

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Second Order Matrix

• a1 b1 a2 b2
• Determinant a1b2 - a2b1

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Second Order Matrix

• a1 b1 a2 b2
• Determinant a1b2 - a2b1

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Third Order Matrix

• a1 b1 c1 a2 b2 c2 a3 b3 c3
• Determinate a1b2c3 b1c2a3 c1a2b3 -
  a3b2c1 - b3c2a1 - c3a2b1

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Third Order Matrix

• a1 b1 c1 a2 b2 c2 a3 b3 c3
• Determinate a1b2c3 b1c2a3 c1a2b3 -
  a3b2c1 - b3c2a1 - c3a2b1

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Third Order Matrix

• a1 b1 c1 a2 b2 c2 a3 b3 c3
• Determinate a1b2c3 b1c2a3 c1a2b3 -
  a3b2c1 - b3c2a1 - c3a2b1

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Third Order Matrix

• a1 b1 c1 a2 b2 c2 a3 b3 c3
• Determinate a1b2c3 b1c2a3 c1a2b3 -
  a3b2c1 - b3c2a1 - c3a2b1

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Third Order Matrix

• a1 b1 c1 a2 b2 c2 a3 b3 c3
• Determinate a1b2c3 b1c2a3 c1a2b3 -
  a3b2c1 - b3c2a1 - c3a2b1

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Third Order Matrix

• a1 b1 c1 a2 b2 c2 a3 b3 c3
• Determinate a1b2c3 b1c2a3 c1a2b3 -
  a3b2c1 - b3c2a1 - c3a2b1

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Third Order Matrix

• a1 b1 c1 a2 b2 c2 a3 b3 c3
• Determinate a1b2c3 b1c2a3 c1a2b3 -
  a3b2c1 - b3c2a1 - c3a2b1

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Cramers Rule with Two Equations

• a1X b1Y c1
• a2X b2Y c2

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• D Determinant a1 b1 a2 b2
• Dx Determinant c1 b1 c2 b2
• Dy - Determinant a1 c1 a2 c2

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• X Dx / D
• Y Dy /D

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Cramers RuleThree Equations

• a1X b1Y c1Z d1
• a2X b2Y c2Z d2
• a3X b3Y c3Z d3
• X Dx / D
• Y Dy / D
• Z Dz / D

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