1. (Total of 4 marks) Let A be a matrix given by: 1 -1 2 a 3 -3 0o 2 a (a) (3 marks) Find determinant of matrix A. (b) (1 marks) For which values of a is the determinant zero? 2. (Total of 4 marks) Let A be a matrix given by E , and consider the linear vector field F() = AZ. (a) (2 marks) Sketch the image of the unit square under the vector field F. (b) (1 marks) Describe in words the image of the unit square. (i.e. point, line, square, rectangle, triangle, parallelogram,... ) (c) (1 marks) Is this vector-valued function invertible? Why? 3. (Total of 4 marks) For the following unrealistic age structure population: 0.4 0.75 (a) (2 marks) Write the corresponding recursive equations. (b) (2 marks) Write the corresponding matrix equation. 4. (Total of 4 marks) Let A be a matrix given by [_11 . (a) (2 marks) Find its eigenvalues. (b) (2 marks) Find an eigenvector for each eigenvalue