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Find the Area of the following Triangles Determinants Determinants Associated with every square matrix is a whole number called the determinant The Determinant of a Matrix A is denoted by detA or |A| Determinant - a square array of numbers or variables enclosed between parallel vertical bars. **To find a determinant you must have a SQUARE MATRIX!!** Finding a 2 x 2 determinant: a b = ad - bc c d Find the determinant: 5 7 1. 11 8 58 711 40 77 40 77 3 2 2. 1 5 37 35 21 15 2 15 2 17 Expansion by Minors a b d e g h c f i e a h f d b i g f d e c i g h same opp same Always: opp same opp same opp same Finding a 3x3 determinant: Expansion by Minors Method 2 7 3 6. Evaluate 1 5 4 6 9 0 5 4 1 4 1 5 2 7 (3) 9 0 6 0 6 9 Step 1: Expand the matrix into 3 pieces. Step 2: Evaluate each 2x2 matrix. Step 3: Simplify. 2(0 (36)) 7(0 (24)) 3(9 30) 21 Finding a 3x3 determinant: Diagonal method 2 4. 6 4 3 8 7 1 5 9 Step 1: Rewrite first two columns of the matrix. -224 +10 +162 = -52 2 3 8 2 3 4. 6 7 1 6 7 4 5 9 4 5 Step 2: multiply diagonals going up! Step 2: multiply diagonals going down! -126 +12 +240 =126 126 - (-52) 126 + 52 = 178 Step 3: Bottom minus top! -18 +50 +6 = 38 Step 2: multiply 5 1 2 5 1 diagonals going up! 5. 2 3 5 2 3 3 2 3 3 2 Step 2: multiply diagonals going down! 45 - 15 + 8 = 38 38 - 38 =0 Step 3: Bottom minus top! Do Now: Copy down this problem. Find the area of a triangle whose vertices are located at (-1, 6), (2, 4), (0, 0).