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det(A - XE) e™A B = A - λι Ε e™A = B² = = e -I −(A³ +3A² + 3A + 1) || = A +E= -3 ܘ -9 IB e¹(B-E) = е-¹eT. =e 1 + 3x 9x 0 1 0 0 0 3 - - -3x = e 3x² 2 9x² 2 en = X 1 3x -(A+1)³ = 0 3 1 -3 0 1 9 3 -3 B³ = 0, -I - (E+ 2B + — ² B²) -1 -x+ X 2 1 - 3x + 3x² 2

det(A - XE) e™A B = A - λι Ε e™A = B² = = e -I −(A³ +3A² + 3A + 1) || = A +E= -3 ܘ -9 IB e¹(B-E) = е-¹eT. =e 1 + 3x 9x 0 1 0 0 0 3 - - -3x = e 3x² 2 9x² 2 en = X 1 3x -(A+1)³ = 0 3 1 -3 0 1 9 3 -3 B³ = 0, -I - (E+ 2B + — ² B²) -1 -x+ X 2 1 - 3x + 3x² 2

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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When calculating the exA of a matrix A, when does A equal to (B-E) or (B+E)? in differential equations?

I have attached an image of the matrix and the solution, after taking the exponents of B I really dont understand whats being done, please if able explain it in more detail. Thank you in advance.

A 2 -3 9 1 1 -1 1 3 -4 -1 -1
Transcribed Image Text:A 2 -3 9 1 1 -1 1 3 -4 -1 -1
det(A - XE) e™A B = A - λι Ε e™A = B² = = e -I −(A³ +3A² + 3A + 1) || = A +E= -3 ܘ -9 IB e¹(B-E) — e-ªeª. =e 1 + 3x 9x 0 1 0 0 0 3 - - -3x = e 3x² 2 9x² 2 en = X 1 3x -(A+1)³ = 0 3 1 -3 0 1 9 3 -3 B³ = 0, -I - (E+ 2B + ²/² B²) -1 -x+ X 2 1 - 3x + 3x² 2
Transcribed Image Text:det(A - XE) e™A B = A - λι Ε e™A = B² = = e -I −(A³ +3A² + 3A + 1) || = A +E= -3 ܘ -9 IB e¹(B-E) — e-ªeª. =e 1 + 3x 9x 0 1 0 0 0 3 - - -3x = e 3x² 2 9x² 2 en = X 1 3x -(A+1)³ = 0 3 1 -3 0 1 9 3 -3 B³ = 0, -I - (E+ 2B + ²/² B²) -1 -x+ X 2 1 - 3x + 3x² 2
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