Question: 2. [2 pts each] Suppose that B and C are square matrices of size n and that N is an invertible square matrix of size

2. [2 pts each] Suppose that B and C are square matrices of size n and that N is an invertible square matrix of size n such that C = N-IBN. (a) Find a formula expressing B in terms of N and C. (b) Show that (2 = N-1B2N. (c) Suppose that D is a diagonal matrix with real entries. If we want to find a diagonal matrix C with real entries such that C? = D, what has to be true about the eigenvalues of D? (d) Let A = 16 -10 50 29 Find a real matrix B with B2 = A (i.e., a square root of A)

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