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Cramer’s Rule for Matrices

Cramer’s Rule for Matrices. You can use properties of matrix determinants for a variety of applications. Today: Solving 3 variable systems of equations with Cramer’s rule for determinants Finding the area of a triangle using Cramer’s rule for determinants. Cramer’s Rule – Systems of Equations.

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Cramer’s Rule for Matrices

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  1. Cramer’s Rule for Matrices • You can use properties of matrix determinants for a variety of applications. • Today: • Solving 3 variable systems of equations with Cramer’s rule for determinants • Finding the area of a triangle using Cramer’s rule for determinants

  2. Cramer’s Rule – Systems of Equations • Solve the following system of equations by the old “elimination” method: • x + 4y –z = 6 • 2x – y + z = 3 • 3x +2y + 3z = 16

  3. Cramer’s Rule – Systems of Equations • We know from the elimination method that x=1, y=2, and z=3 • Now by Cramer’s Rule: • Set up a 3x3 matrix using only the coefficients. • Find the determinant of the matrix. • Replace any column of coefficients with the column of answers. • Find the determinant of the slightly altered matrix. • Divide the two determinants out for your variable’s value. • Repeat process for the other two variables.

  4. Cramer’s Rule – Systems of Equations • Practice this by Cramer’s Rule: • 2x + 4y – 3z = 1 • 3x – 2y + 5z = 8 • x + 7y – 2z = -9

  5. Other Applications of the Determinant • Given the Following Coordinate Geometry Triangle: • A (1,1) • B (2,6) • C (5,2) • Find by boxing it in on graph paper and creating a series of right triangles.

  6. Other Applications of the Determinant • Now we’ll solve by using the properties of a determinant. • Set up a matrix • We need an additional row to find a determinant. • Once we have the determinant, let’s use an old Area of a triangle formula

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