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Problem 4. Given a scalar a, the exponential e" can be expanded by Taylor series as: 4 1 1 1 =1+a+ ·a + a + a +... 2! 3! 4! eª Similarly, we define the matrix exponential e of any n x n matrix A as 1 1 4! (b) 1 e¹ = I + A+ A² 2! If A is diagonalizable to a diagonal matrix D, (a) Express e¹ by e. 1 Compute e for A = 0 1 1 1 0 0 1 2 + 3! A³ + Aª +... 14

Problem 4. Given a scalar a, the exponential e" can be expanded by Taylor series as: 4 1 1 1 =1+a+ ·a + a + a +... 2! 3! 4! eª Similarly, we define the matrix exponential e of any n x n matrix A as 1 1 4! (b) 1 e¹ = I + A+ A² 2! If A is diagonalizable to a diagonal matrix D, (a) Express e¹ by e. 1 Compute e for A = 0 1 1 1 0 0 1 2 + 3! A³ + Aª +... 14

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 4. Given a scalar a, the exponential eº can be expanded by Taylor series as: 1 1 1 2 eª = 1+ a + a + a + ·a +... 2! 3! 4! Similarly, we define the matrix exponential e of any n x n matrix A as 1 1 1 e¹ = I + A+ A¹² + A³ + At +... 2! 3! 4! (b) If A is diagonalizable to a diagonal matrix D, (a) Express e¹ by P. 1 1 1 CH 0 0 1 2 Compute e for A=0
Transcribed Image Text:Problem 4. Given a scalar a, the exponential eº can be expanded by Taylor series as: 1 1 1 2 eª = 1+ a + a + a + ·a +... 2! 3! 4! Similarly, we define the matrix exponential e of any n x n matrix A as 1 1 1 e¹ = I + A+ A¹² + A³ + At +... 2! 3! 4! (b) If A is diagonalizable to a diagonal matrix D, (a) Express e¹ by P. 1 1 1 CH 0 0 1 2 Compute e for A=0
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