Precalculus Problem Set 53 Name __________________________ 7.4 - Applications of Determinants and Matrices 1. Use a determinant to find the area of the triangle with vertices (0, 2), (1, 4), (3,5). 2. Use a determinant to find the area of the triangle with vertices (2, 4), (1,5), (3, 2). 3. Find the value of x such that the triangle with vertices (4, 2), (3,5), (1, x ) has an area of 4. 4. Use Cramer's Rule (if possible) to solve the following system: 4 x 2 y 3z 2 2 x 2 y 5 z 16 8x 5 y 2 z 4 5. Use Cramer's Rule (if possible) to solve the following system: 2 x 3 y 5z 4 3x 5 y 9 z 7 5 x 9 y 17 z 13 6. Use a determinant to determine if the following points are collinear: (2,3), (3,3.5), (1,2). 7. Use the method of finite differences to determine a polynomial model. x y 1 2 3 4 5 6 7 1 2 4 8 16 31 57 9. Find the position equation s t 1 sec, s 452 ft t 2 sec, s 260 ft t 3 sec, s 116 ft 1 2 at v0t s0 . 2