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4.3 Determinants and Cramer’s Rule

4.3 Determinants and Cramer’s Rule. Algebra 2. Definition. Determinate- A real number associated with any square matrix. The Determinate of a Matrix. Determinate of a 2x2 matrix Determinate of a 3x3 matrix =. Examples. Find the determinate of the following matrices. Example.

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4.3 Determinants and Cramer’s Rule

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  1. 4.3 Determinants and Cramer’s Rule Algebra 2

  2. Definition • Determinate- A real number associated with any square matrix

  3. The Determinate of a Matrix • Determinate of a 2x2 matrix • Determinate of a 3x3 matrix =

  4. Examples • Find the determinate of the following matrices

  5. Example • Find the area of the triangle with coordinates (2, 4), (5, 1), and (2, -2)

  6. Area of a Triangle • The area of a triangle with vertices , is given by

  7. Example • Find the area of the triangle with coordinates (2, 4), (5, 1), and (2, -2)

  8. Example • Find the area of the triangle with vertices (5, -2), (3, 3)

  9. Cramer’s Rule • Cramer’s rule: a method (named after a Swiss mathematician Gabriel Cramer) used to solve linear equations Linear System Coefficient Matrix

  10. Cramer’s Rule for a 2x2 matrix • Let A be the coefficient matrix of this linear system If then the system has exactly one solution. The solution is : and

  11. Example • Use Cramer’s rule to solve the systems below:

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