DETERMINANTS

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DETERMINANTS
SECTION 6.3
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DETERMINANTS
2 X 2 Matrices Det A ad - bc
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SIGN CONVENTION
We associate a plus or minus sign with every
position in a matrix.
3 X 3 Matrices
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SIGN CONVENTION
We associate a plus or minus sign with every
position in a matrix.
4 X 4 Matrices
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EXAMPLE
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EXAMPLE
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EXAMPLE
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EXAMPLE
- 3 8 - 6 - 2 2 10 3 - 3 - 20 -
6 - 24 - 69 - 99
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DETERMINANTS ON CALCULATOR
DET A 154
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EXAMPLE
Solve for x
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EXAMPLE
x 2 (2 - 6) - x (1 - 12) 1 (2 - 8) 0 - 4 x 2
11x - 6 0 x 3/4 x 2
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CRAMERS RULE
For the system ax by s cx dy t D
Dx Dy
The solution is x y
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AN IMPORTANT CONCLUSION

• If the determinant of the coefficient matrix is
  0, the system has no unique solution.
• This means that the system is either inconsistent
  (has no solution) or it is dependent (has
  infinitely many solutions.

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CRAMERS RULE
a11x a12y a13z c1 a21x a22y a23z
c2 a31x a32y a33z c3
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CRAMERS RULE
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CRAMERS RULE
The solution is x y z
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EXAMPLES
Do Problems 34, 36, and 38.
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• CONCLUSION OF SECTION 6.3