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4.3 Determinants and Cramer’s Rule

Learn about determinants, their evaluation, and Cramer’s Rule for solving systems of linear equations using determinants. Explore how determinants determine the number of solutions in a system and find the point of intersection using Cramer’s Rule.

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4.3 Determinants and Cramer’s Rule

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  1. 4.3 Determinants and Cramer’s Rule

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

  3. Evaluate each determinant. 1. 2. 3.

  4. 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

  5. Cramer’s 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.

  6. Use Cramer’s Rule to solve the system. • 5. D= D= Dx= Dx= Dy= Dy= Point of Intersection: Point of Intersection:

  7. Use Cramer’s Rule to solve the system. 6. 7. D= D= Dx= Dx= Dy= Dy= Point of Intersection: Point of Intersection:

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