2. 5x -4y a) Solve for x and y based on Cramer's Rule of Determinants: 3x + 2y 5, Answer: x 1, y = 1 b) Solve for x and y based on Matrix Inversion: x - 2 y = - 4, 4x y = 5 Answer: x 2, y = 3 c) Solve for x, y, and z: Answer: x = -1, y = 1, z = 2 3x-3y + 2z= - 2 x+2y - z-1, 3, 2x - y + 3z

Use determinants to solve the matrix equation Ax = b where 0 -1 -1 Enter the vector x in the form [X₁, X2, X3]: A= = - -1 1 3 -5 1 -1 b = -7 -5 -15

Fill in the blanks with appropriate numbers to calculate the determinant. (a) 9 - • 4 = %3D 1 -1 -3 (b) = ? v1 : O: -3) = 3 -4 1 • 0 - • 2) 3 . -3) • 1 - 2

Pr. #1) Find A-1, if it exists. 3 A = -5 -11 Pr. #2) Find the determinant of A. 1 -2 3 A = 7 6 -3 4 1 Pr. #3) The system of linear equations has a unique solution. Find the solution using Cramer's Rule. 2т — Зу — 5 -3x + 8y = 3 Pr. #4) Find the solution to the system, or show that it does not exist. x² + y² = 20 3x – y = 2