<p>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</p><p>DIAGONALS METHOD</p><p>Given matrix </p><p>Rewrite the matrix repeating columns 1 and 2 to get .</p><p>Draw three diagonals of three elements beginning with the upper right-hand element.</p><p>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.</p><p>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 .</p><p>COFACTORS METHOD</p><p>Given matrix </p><p> det .</p><p>Examples:</p><p>1. </p><p>2.</p><p>2 Acc. Math 2 Name______Matrices—Finding Determinants of 3 X 3 Matrices & Using to Find Area of Triangles</p><p>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.</p><p>Given a triangle with vertices , and , the area of the triangle is the absolute value of the number found by using </p><p>Acc. Math 2 Name______Matrices—Finding Determinants of 3 X 3 Matrices & Using to Find Area of Triangles</p><p>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.</p><p>Given a triangle with vertices , and , the area of the triangle is the absolute value of the number found by using </p><p>3 Notes on Matrices—Inverses Acc. Math 2</p><p>Example: 3. Find the area of a triangle with vertices , and .</p><p>Example: 3. Find the area of a triangle with vertices , and .</p><p>4</p>