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4. Let A²-k²In, = for a real number k. Find a closed form formula for e^ = I + A + ² + ³² + …... Justify your answer.

4. Let A²-k²In, = for a real number k. Find a closed form formula for e^ = I + A + ² + ³² + …... Justify your answer.

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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A²=-R²I₂. If K²=0, then A²=0 and hence 423,2 A = 0₁ A So e ² = I+ A+ A² + A³: 21 + A² 3 = I+ A. Let R²70. Than A²=-k²I; A²³=_k²A; A² = R²I; A² = R²^A;... A² ал агень Thus ² = I+ A+ A² + A³ +AT+AS 21 31 H l, 2e (-1) RA. • B (1-1² + R² - k²² + - .) I 41 + (1 + (-1²) A² + 1² A-²/²³^) --- ) 71 ($-4² +24 *+--) I .) (-1) I 61 + * (R-1₁² + 45 -12²2 +--) A ( EXPLAIN 1) 31 51 = (Cos R) I₂ + Sink A. why? why?
Transcribed Image Text:A²=-R²I₂. If K²=0, then A²=0 and hence 423,2 A = 0₁ A So e ² = I+ A+ A² + A³: 21 + A² 3 = I+ A. Let R²70. Than A²=-k²I; A²³=_k²A; A² = R²I; A² = R²^A;... A² ал агень Thus ² = I+ A+ A² + A³ +AT+AS 21 31 H l, 2e (-1) RA. • B (1-1² + R² - k²² + - .) I 41 + (1 + (-1²) A² + 1² A-²/²³^) --- ) 71 ($-4² +24 *+--) I .) (-1) I 61 + * (R-1₁² + 45 -12²2 +--) A ( EXPLAIN 1) 31 51 = (Cos R) I₂ + Sink A. why? why?
4. Let A²-k²In, for a real number k. Find a closed form formula for e^ = I + A+²+³+…... Justify your answer. CA
Transcribed Image Text:4. Let A²-k²In, for a real number k. Find a closed form formula for e^ = I + A+²+³+…... Justify your answer. CA
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