Problem 4. Given a scalar a, the exponential eº can be expanded by Taylor series as: (b) eª 1 =1+a+ -a² +· 2! 3! Similarly, we define the matrix exponential e of any n x n matrix A as 1 1 1 e¹ = I + A+ -A²+ A³ + 2! 3! 4! If A is diagonalizable to a diagonal matrix D, (a) Expressed by e. 1 Compute e for A = 0 1 1 3 a³ + a +... 4! 1 0 1 012 +...

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