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Evaluating Determinants and Triangle Areas: Cramer's Rule Simplified

This comprehensive guide explains how to evaluate the determinants of 2x2 and 3x3 matrices and find the area of a triangle given its vertices. Learn the efficient methods to compute matrix determinants using diagonal multiplication and Cramer's Rule to solve linear systems. We detail the steps to find determinants of coefficient matrices and provide clear instructions on substituting variables for solutions. Perfect for students and anyone looking to strengthen their understanding of linear algebra concepts.

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Evaluating Determinants and Triangle Areas: Cramer's Rule Simplified

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  1. Notes Over 4.3 Evaluate Determinants of 2 x2 Matrices Stands for the determinant of a matrix. Multiply diagonally, down first. Opposite products going up.

  2. Notes Over 4.3 Evaluate Determinants of 3 x3 Matrices Repeat the first two columns. Multiply diagonally, down first. Opposite products going up.

  3. Notes Over 4.3 The Area of a Triangle Find the area of the triangle with the given vertices.

  4. Notes Over 4.3 The Area of a Triangle Find the area of the triangle with the given vertices.

  5. Notes Over 4.3 The Area of a Triangle Find the area of the triangle with the given vertices.

  6. Notes Over 4.3 The Area of a Triangle Find the area of the triangle with the given vertices.

  7. Notes Over 4.3 Using Cramer’s Rule for a 2 x 2 System Use Cramer’s Rule to solve the linear system. Find the determinant of the coefficient Matrix To find your x replace the x ’s in the coefficient Matrix with the constants To find your y replace the y ’s in the coefficient Matrix with the constants

  8. Notes Over 4.3 Using Cramer’s Rule for a 2 x 2 System Use Cramer’s Rule to solve the linear system. Find the determinant of the coefficient Matrix To find your x replace the x ’s in the coefficient Matrix with the constants To find your y replace the y ’s in the coefficient Matrix with the constants

  9. Notes Over 4.3 Using Cramer’s Rule for a 2 x 2 System Use Cramer’s Rule to solve the linear system. Find the determinant of the coefficient Matrix To find your x replace the x ’s in the coefficient Matrix with the constants To find your y replace the y ’s in the coefficient Matrix with the constants

  10. Notes Over 4.3 Using Cramer’s Rule for a 2 x 2 System Use Cramer’s Rule to solve the linear system. Find the determinant of the coefficient Matrix To find your x replace the x ’s in the coefficient Matrix with the constants To find your y replace the y ’s in the coefficient Matrix with the constants

  11. Notes Over 4.3 Using Cramer’s Rule for a 2 x 2 System Use Cramer’s Rule to solve the linear system. Find the determinant of the coefficient Matrix To find your x replace the x ’s in the coefficient Matrix with the constants To find your y replace the y ’s in the coefficient Matrix with the constants

  12. Notes Over 4.3 Using Cramer’s Rule for a 2 x 2 System Use Cramer’s Rule to solve the linear system. Find the determinant of the coefficient Matrix To find your x replace the x ’s in the coefficient Matrix with the constants To find your y replace the y ’s in the coefficient Matrix with the constants

  13. Notes Over 4.3

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