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22 - 62 + 11 = 0 and by the theorem you have A² - 6A + 111, = 0 1 -3 A = strate the Cayley-Hamilton Theorem for the matrix A given below. 0 2 -1 A = -1 5 -1 0 0 1 1: Find and expand the characteristic equation. 2: Compute the required powers of A. - EBB |-2 10 A² = 23 |-10 46 -11 A³ = -23 105 -23 1 3: Write a matrix version of the characteristic equation by replacing 2 with A. (Use I for the 3x3 identity matrix.)

22 - 62 + 11 = 0 and by the theorem you have A² - 6A + 111, = 0 1 -3 A = strate the Cayley-Hamilton Theorem for the matrix A given below. 0 2 -1 A = -1 5 -1 0 0 1 1: Find and expand the characteristic equation. 2: Compute the required powers of A. - EBB |-2 10 A² = 23 |-10 46 -11 A³ = -23 105 -23 1 3: Write a matrix version of the characteristic equation by replacing 2 with A. (Use I for the 3x3 identity matrix.)

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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The Cayley-Hamilton Theorem states that a matrix satisfies its characteristic equation. For example, the characteristic equation of the matrix shown below is as follows. 12 - 6) + 11 = 0 and by the theorem you have A² - 6A + 11I, = 0 1 -3 A = 2 5 Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 0 2 -1 A = -1 5 -1 0 0 1 STEP 1: Find and expand the characteristic equation. STEP 2: Compute the required powers of A. |-2 10 -3 A2 = |-5 23 -5 1 ⒤둥⒤갓⒤갓⒤빨⒤ |-10 46 -11 A3 = |-23 105 -23 1 STEP 3: Write a matrix version of the characteristic equation by replacing 2 with A. (Use I for the 3x3 identity matrix.)
Transcribed Image Text:The Cayley-Hamilton Theorem states that a matrix satisfies its characteristic equation. For example, the characteristic equation of the matrix shown below is as follows. 12 - 6) + 11 = 0 and by the theorem you have A² - 6A + 11I, = 0 1 -3 A = 2 5 Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 0 2 -1 A = -1 5 -1 0 0 1 STEP 1: Find and expand the characteristic equation. STEP 2: Compute the required powers of A. |-2 10 -3 A2 = |-5 23 -5 1 ⒤둥⒤갓⒤갓⒤빨⒤ |-10 46 -11 A3 = |-23 105 -23 1 STEP 3: Write a matrix version of the characteristic equation by replacing 2 with A. (Use I for the 3x3 identity matrix.)
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