12. Let a matrix A = (1 +21 = (a) Compute the characteristic roots (eigenvalues) of matrix A. (6 marks) < (b) Compute th

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12 Let A Matrix A 1 21 A Compute The Characteristic Roots Eigenvalues Of Matrix A 6 Marks B Compute Th 1 (37.43 KiB) Viewed 26 times

12. Let a matrix A = (1 +21 = (a) Compute the characteristic roots (eigenvalues) of matrix A. (6 marks) < (b) Compute the characteristic vectors (eigenvectors) of matrix A, normalising the solution for vv = 1 for both vectors i = 1,2. (10 marks) EC206 2021/2 A 800 Turn over Page 9 (c) Use the obtained eigenvalues to calculate the trace and the determinant of matrix A. What does this imply for the rank of the matrix? (5 marks) (d) Verify the previous results obtained in (c)) by alternative means. (4 marks) (e) Assuming that matrix A defines a coefficient matrix in a linear- equation system, how many solutions should this system have and why? (5 marks)