Given A = 0 . If the eigenvalues of A are 3 and 5, then a b a Hint: sum of eigenvalues is related to the trace, product of eigenvalues is related to the determinant. O' 1 Given B = 0 0 1 . If the eigenvalues of B are 1, 2 and -1, then C d e C Use the same hint as above. From the relation between sum of eigenvalues and the trace you should get e easily; and from the relation between product of eigenvalues and the determinant you should get c without too much difficulty (assuming you know which row/column to choose to expand to get the determinant); the value of d is harder to get: after you find c, e, then you plug them as well as any one eigenvalue of B in | B - XI| = 0, this equation will be solely on d, solve it to get d