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4.3: Determinants and the Area of a triangle using a matrix

4.3: Determinants and the Area of a triangle using a matrix. Objectives: Students will be able to… Find the determinant of a 2x2 matrix and a 3.3 matrix Find the area of a triangle on the coordinate plane using a matrix. Determinant. A real number associated with a square matrix

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4.3: Determinants and the Area of a triangle using a matrix

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  1. 4.3: Determinants and the Area of a triangle using a matrix Objectives: Students will be able to… Find the determinant of a 2x2 matrix and a 3.3 matrix Find the area of a triangle on the coordinate plane using a matrix

  2. Determinant • A real number associated with a square matrix • Determinant for Matrix A denoted by det A or |A| • DETERMINANT FOR A 2 X 2 MATRIX: • ad – cb • (Difference of the products of the entries on the diagonals)

  3. Example: • Evaluate the determinant for the matrix below.

  4. Determinant for a 3 x 3 matrix • Rewrite the first 2 columns to the right of the determinant • Subtract the sum of the products in red from the products in blue. • a b • det d e • g h • = (aei + bfg + cdh) – (gec + hfa + idb)

  5. Evaluate the determinant

  6. Example

  7. Area of a triangle • The area of a triangle with vertices (x1,y1), (x2,y2), and (x3,y3) is given by: • Area = • ±choose appropriate sign to yield a positive value

  8. Find the area of a triangle with the following vertices • (5, -2) (3, 3) (-4,1)

  9. The cities of San Francisco (-30, 32), Oakland (-16,40), and San Jose (0,0) form a triangular shaped area. Estimate the area formed by the 3 cities.

  10. To find determinant on calculator • Enter Matrix • Matrix MATH 1:det( Enter name of matrix

  11. What is the difference between the following:

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