4.3 Determinants and Cramer

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4.3 Determinants and Cramers Rule
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Determinants

• The of the matrix , symbolized
• Note that the vertical bars are not absolute
  value signs, it is notation for determinant.

has the value
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Evaluate each determinant.

• 1. 2. 3.

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Given the system of equations with the
coefficient matrix
The determinant of The x coefficients are The y
coefficients are the coefficient matrix replaced
with the replaced with the constants
constants
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Cramers Rule for a System

• Given the system of linear equations
• If the D 0, then the system has exactly one
  solution. The solution is
• Note If D 0, the system has either no
  solution or infinitely many solutions.

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Use Cramers Rule to solve the system.

• 5.
• D D
• Dx Dx
• Dy Dy
• Point of Intersection Point of Intersection

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Use Cramers Rule to solve the system.

• 6. 7.
• D D
• Dx Dx
• Dy Dy
• Point of Intersection Point of Intersection