Acc. Math 2 Name______Matrices—Finding Determinants of 3 X 3 Matrices & Using to Find Area of Triangles Georgia Performance Standard: MM3A4: Students will perform basic operations with matrices. Vocabulary: matrix (matrices) element (entry) naming a matrix dimensions row matrix column matrix square matrix zero matrix equal matrices matrix addition matrix subtraction scalar & scalar multiplication matrix multiplication product matrix transposition on a matrix identity matrix inverse matrices main diagonal invertible (nonsingular) singular determinant

DIAGONALS METHOD

Given matrix

Rewrite the matrix repeating columns 1 and 2 to get .

Draw three diagonals of three elements beginning with the upper right-hand element.

Find the products of the elements in each diagonal and add these products. aei + bfg + cdh Draw three diagonals of three elements beginning with the lower right-hand element.

Find the products of the elements in each diagonal and add these products. 1 Notes on Matrices—Inverses Acc. Math 2 gec + hfa + idb (aei + bfg + cdh) (gec + hfa + idb) is the det .

COFACTORS METHOD

Given matrix

det .

Examples:

1.

2.

2 Acc. Math 2 Name______Matrices—Finding Determinants of 3 X 3 Matrices & Using to Find Area of Triangles

AREA OF A TRIANGLE The determinant of a 3 X 3 matrix can be used to find the area of a triangle given the vertices of the triangle.

Given a triangle with vertices , and , the area of the triangle is the absolute value of the number found by using

Acc. Math 2 Name______Matrices—Finding Determinants of 3 X 3 Matrices & Using to Find Area of Triangles

AREA OF A TRIANGLE The determinant of a 3 X 3 matrix can be used to find the area of a triangle given the vertices of the triangle.

Given a triangle with vertices , and , the area of the triangle is the absolute value of the number found by using

3 Notes on Matrices—Inverses Acc. Math 2

Example: 3. Find the area of a triangle with vertices , and .

Example: 3. Find the area of a triangle with vertices , and .

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