Question: 3 0 0 2 5 n 2 -1 Consider the matrix A= m where m and n are constants. (i) Given that 5 is

3 0 0 2 5 n 2 -1 Consider the matrix A=

3 0 0 2 5 n 2 -1 Consider the matrix A= m where m and n are constants. (i) Given that 5 is an eigenvector of A and find the associated eigenvalue. 2 (ii) Given that -3 is also an eigenvalue of A. Find the associated eigenvector. (iii) Given that 1 is also an eigenvector of A. Find the associated eigenvalue, the value of m and the value of n. (iv) Find a nonsingular matrix P and a diagonal matrix D such that A = PDP-.

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